From 1fd2213192d22880706440e7f724bdc6db966ee0 Mon Sep 17 00:00:00 2001 From: Juan Marin Noguera Date: Tue, 22 Aug 2023 17:56:56 +0200 Subject: Añadida presentación MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- present/fig/cat-assoc.svg | 83 +++++++++ present/fig/cat-assoc.tex | 16 ++ present/fig/cat-ident.svg | 79 +++++++++ present/fig/cat-ident.tex | 17 ++ present/fig/convert.sh | 5 + present/fig/couniversal.svg | 86 ++++++++++ present/fig/couniversal.tex | 16 ++ present/fig/front.svg | 361 ++++++++++++++++++++++++++++++++++++++++ present/fig/front.tex | 28 ++++ present/fig/head.tex | 128 ++++++++++++++ present/fig/monad_data.svg | 72 ++++++++ present/fig/monad_data.tex | 16 ++ present/fig/monad_data_adj.svg | 118 +++++++++++++ present/fig/monad_data_adj.tex | 16 ++ present/fig/monad_data_pow.svg | 135 +++++++++++++++ present/fig/monad_data_pow.tex | 16 ++ present/fig/monad_unit.svg | 97 +++++++++++ present/fig/monad_unit.tex | 17 ++ present/fig/monad_unita_adj.svg | 102 ++++++++++++ present/fig/monad_unita_adj.tex | 17 ++ present/fig/monad_unita_pow.svg | 93 +++++++++++ present/fig/monad_unita_pow.tex | 15 ++ present/fig/monad_unitb_pow.svg | 119 +++++++++++++ present/fig/monad_unitb_pow.tex | 15 ++ present/fig/natural.svg | 106 ++++++++++++ present/fig/natural.tex | 17 ++ present/fig/universal.svg | 86 ++++++++++ present/fig/universal.tex | 16 ++ 28 files changed, 1892 insertions(+) create mode 100644 present/fig/cat-assoc.svg create mode 100644 present/fig/cat-assoc.tex create mode 100644 present/fig/cat-ident.svg create mode 100644 present/fig/cat-ident.tex create mode 100755 present/fig/convert.sh create mode 100644 present/fig/couniversal.svg create mode 100644 present/fig/couniversal.tex create mode 100644 present/fig/front.svg create mode 100644 present/fig/front.tex create mode 100644 present/fig/head.tex create mode 100644 present/fig/monad_data.svg create mode 100644 present/fig/monad_data.tex create mode 100644 present/fig/monad_data_adj.svg create mode 100644 present/fig/monad_data_adj.tex create mode 100644 present/fig/monad_data_pow.svg create mode 100644 present/fig/monad_data_pow.tex create mode 100644 present/fig/monad_unit.svg create mode 100644 present/fig/monad_unit.tex create mode 100644 present/fig/monad_unita_adj.svg create mode 100644 present/fig/monad_unita_adj.tex create mode 100644 present/fig/monad_unita_pow.svg create mode 100644 present/fig/monad_unita_pow.tex create mode 100644 present/fig/monad_unitb_pow.svg create mode 100644 present/fig/monad_unitb_pow.tex create mode 100644 present/fig/natural.svg create mode 100644 present/fig/natural.tex create mode 100644 present/fig/universal.svg create mode 100644 present/fig/universal.tex (limited to 'present/fig') diff --git a/present/fig/cat-assoc.svg b/present/fig/cat-assoc.svg new file mode 100644 index 0000000..8eda971 --- /dev/null +++ b/present/fig/cat-assoc.svg @@ -0,0 +1,83 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/present/fig/cat-assoc.tex b/present/fig/cat-assoc.tex new file mode 100644 index 0000000..b769666 --- /dev/null +++ b/present/fig/cat-assoc.tex @@ -0,0 +1,16 @@ +\documentclass[12pt]{standalone} +\input{head} +\begin{document} +\begin{tikzpicture}\selectlanguage{english} + \path (0,2) node(A) {$a$} (2,2) node(B) {$b$} + (0,0) node(C) {$c$} (2,0) node(D) {$d$}; + \draw[->] (A) -- node[above]{$f$} (B); + \draw[->] (B) -- node[right]{$h\circ g$} (D); + \draw[->] (A) -- node[left]{$g\circ f$} (C); + \draw[->] (C) -- node[below]{$h$} (D); +\end{tikzpicture} +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/present/fig/cat-ident.svg b/present/fig/cat-ident.svg new file mode 100644 index 0000000..f2b1b20 --- /dev/null +++ b/present/fig/cat-ident.svg @@ -0,0 +1,79 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/present/fig/cat-ident.tex b/present/fig/cat-ident.tex new file mode 100644 index 0000000..7fa64de --- /dev/null +++ b/present/fig/cat-ident.tex @@ -0,0 +1,17 @@ +\documentclass[12pt]{standalone} +\input{head} +\begin{document} +\begin{tikzpicture}\selectlanguage{english} + \path (0,2) node(A){$a$} (2,2) node(AP){$a$} + (0,0) node(B){$b$} (2,0) node(BP){$b$}; + \draw[->] (A) -- node[above]{$1_a$} (AP); + \draw[->] (AP) -- node[right]{$f$} (BP); + \draw[->] (A) -- node[left]{$f$} (B); + \draw[->] (B) -- node[below]{$1_b$} (BP); + \draw[->] (A) -- node[above]{$f$} (BP); +\end{tikzpicture} +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/present/fig/convert.sh b/present/fig/convert.sh new file mode 100755 index 0000000..f2018f1 --- /dev/null +++ b/present/fig/convert.sh @@ -0,0 +1,5 @@ +#!/bin/sh +for f in *.pdf +do pdf2svg "$f" "${f%.pdf}.svg" +done + diff --git a/present/fig/couniversal.svg b/present/fig/couniversal.svg new file mode 100644 index 0000000..8e32d9b --- /dev/null +++ b/present/fig/couniversal.svg @@ -0,0 +1,86 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/present/fig/couniversal.tex b/present/fig/couniversal.tex new file mode 100644 index 0000000..dd0feb6 --- /dev/null +++ b/present/fig/couniversal.tex @@ -0,0 +1,16 @@ +\documentclass[12pt]{standalone} +\input{head} +\begin{document} +\begin{tikzpicture}\selectlanguage{english} + \path (0,-2) node(B){$c$} (-2,-2) node(UC){$Tb$} (-4,-2) node(C){$b$}; + \path (-2,0) node(UX){$Tx$} (-4,0) node(X){$x$}; + \draw[<-] (B) -- node[below]{$v$} (UC); + \draw[<-] (B) -- node[right]{$g$} (UX); + \draw[<-,dotted] (UC) -- node[left]{$T\hat g$} (UX); + \draw[<-,dotted] (C) -- node[left]{$\hat g$} (X); +\end{tikzpicture} +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/present/fig/front.svg b/present/fig/front.svg new file mode 100644 index 0000000..0af604b --- /dev/null +++ b/present/fig/front.svg @@ -0,0 +1,361 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/present/fig/front.tex b/present/fig/front.tex new file mode 100644 index 0000000..ce4406e --- /dev/null +++ b/present/fig/front.tex @@ -0,0 +1,28 @@ +\documentclass[12pt]{standalone} +\input{head} +\begin{document} +\begin{tikzpicture}[scale=1.8]\selectlanguage{english} + \path (0,4) node(SS){$S'Sb$} (2,4) node(TS){$T'Sb$} (4,4) node(US){$U'Sb$}; + \path (2,2) node(TT){$T'Tb$} (4,2) node(UT){$U'Tb$}; + \path (4,0) node(UU){$U'Ub$}; + \draw[->] (SS) -- node[above]{$\sigma'_{Sb}$} (TS); + \draw[->] (TS) -- node[above]{$\tau'_{Sb}$} (US); + \draw[->] (US) -- node[right]{$U'\sigma_b$} (UT); + \draw[->] (UT) -- node[right]{$U'\tau_b$} (UU); + \draw[->] (TS) -- node[right]{$T'\sigma_b$} (TT); + \draw[->] (TT) -- node[above]{$\tau'_{Tb}$} (UT); + \draw[->] (SS) -- node[above]{$\sigma'\circ\sigma$} (TT); + \draw[->] (TT) -- node[above]{$\tau'\circ\tau$} (UU); + \path (0,2) node(ST){$S'Tb$} (0,0) node(SU){$S'Ub$} (2,0) node(TU){$T'Ub$}; + \draw[->] (SS) -- node[left]{$S'\sigma_b$} (ST); + \draw[->] (ST) -- node[left]{$S'\tau_b$} (SU); + \draw[->] (SU) -- node[below]{$\sigma'_{Ub}$} (TU); + \draw[->] (TU) -- node[below]{$\tau'_{Ub}$} (UU); + \draw[->] (ST) -- node[below]{$\sigma'_{Tb}$} (TT); + \draw[->] (TT) -- node[left]{$T'\tau_b$} (TU); +\end{tikzpicture} +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/present/fig/head.tex b/present/fig/head.tex new file mode 100644 index 0000000..8e7724a --- /dev/null +++ b/present/fig/head.tex @@ -0,0 +1,128 @@ +\usepackage[utf8]{inputenc} +\usepackage[english,spanish]{babel} +\usepackage{microtype} +%\renewcommand{\fullwidthdisplay}{} + +% Formatting +\usepackage{tikz} + +\newenvironment{diagram}{\begin{tikzpicture}\selectlanguage{english}}{\end{tikzpicture}} +\usetikzlibrary{decorations.pathmorphing} +\newcommand{\tikzsquig}{\draw[->, +line join=round, +decorate, decoration={ + zigzag, + segment length=4, + amplitude=.9,post=lineto, + post length=2pt +}]} % https://tex.stackexchange.com/questions/12678/squiggly-arrows-in-tikz#12680 + +% Math packages +\usepackage{mathtools} +\usepackage{amsthm} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{stackrel} + +% Theorem styles +%\newtheorem{proposition}{Proposición}[chapter] +%\newtheorem{theorem}[proposition]{Teorema} +%\newtheorem{corollary}[proposition]{Corolario} +%\newtheorem{lemma}[proposition]{Lema} +%\theoremstyle{definition} +%\newtheorem{definition}[proposition]{Definición} +%\newtheorem{axiom}[proposition]{Axioma} +%\theoremstyle{remark} +%\newtheorem{example}[proposition]{Ejemplo} + +% Math macros +\newcommand{\E}{\text{e}} +\newcommand{\I}{\text{i}} +\newcommand{\dash}{\text{-}} +\newcommand{\dCat}[2]{\newcommand{#1}{{\bf #2}}} +\newcommand{\conc}[1]{\emph{#1}\newglossaryentry{#1}{name=#1,description={\,}}} +\newcommand{\concsuffix}[1]{\emph{#1}} +\newcommand{\eps}{\varepsilon} +\dCat{\bAlg}{Alg} +\dCat{\bSet}{Set} +\dCat{\bRel}{Rel} +\dCat{\bPrord}{Prord} +\dCat{\bOrd}{Ord} +\dCat{\bLat}{Lat} +\dCat{\bGrph}{Grph} +\dCat{\bMGrph}{MGrph} +\dCat{\bMat}{Mat} +\dCat{\bSmgrp}{Smgrp} +\dCat{\bMon}{Mon} +\dCat{\bGrp}{Grp} +\dCat{\bAb}{Ab} +\dCat{\bRing}{Rng} % Backwards compat +\dCat{\bRng}{Rng} +\dCat{\bCRng}{CRng} +\dCat{\bDom}{Dom} +\dCat{\bField}{Field} +\dCat{\bMod}{Mod} +\dCat{\bVec}{Vec} +\dCat{\bVecf}{Vec_f} +\dCat{\bTop}{Top} +\dCat{\bTopm}{Top_m} +\dCat{\bMetc}{Met_c} +\dCat{\bMetu}{Met_u} +\dCat{\bMet}{Met} +\dCat{\bBanu}{Ban} +\dCat{\bBan}{Ban} +\dCat{\bBanb}{Ban_b} +\dCat{\bZero}{0} +\dCat{\bOne}{1} +\dCat{\bTwo}{2} +\dCat{\bDown}{\downarrow} +\dCat{\bDDown}{\downdownarrows} +\dCat{\bCat}{Cat} +\dCat{\bCAT}{CAT} +\dCat{\bCls}{Cls} +\dCat{\bTopVec}{TopVec} +\dCat{\bType}{Type} +\newcommand{\cA}{\mathcal{A}} +\newcommand{\cB}{\mathcal{B}} +\newcommand{\cC}{\mathcal{C}} +\newcommand{\cD}{\mathcal{D}} +\newcommand{\cS}{\mathcal{S}} +\newcommand{\dKey}[2]{\newcommand{#1}{\text{#2}}} +\newcommand{\dKeyPar}[2]{\newcommand{#1}[1]{\text{#2}({##1})}} +\dKeyPar{\Ob}{Ob} +\dKeyPar{\Mor}{Mor} +\dKeyPar{\Mnd}{Mnd} +\dKey{\dom}{dom} +\dKey{\cod}{cod} +\dKey{\Img}{Im\,} +\newcommand{\dStdSet}[2]{\newcommand{#1}{\mathbb{#2}}} +\dStdSet{\sNat}{N} +\dStdSet{\sInt}{Z} +\dStdSet{\sRat}{Q} +\dStdSet{\sReal}{R} +\dStdSet{\sComplex}{C} +\dStdSet{\sCirc}{S} +\dStdSet{\sTorus}{T} +\newcommand{\monicTo}{\rightarrowtail} +\newcommand{\epicTo}{\twoheadrightarrow} +\newcommand{\inTo}{\hookrightarrow} +\renewcommand{\mapsto}{\rightsquigarrow} +\renewcommand{\Im}{\error{You probably meant \backslash{}Img}} +\newcommand{\dual}[1]{#1^{\mathrm{op}}} +\newcommand{\power}{\mathcal{P}} +\newcommand{\copower}{\mathcal{Q}} +\newcommand{\UNIVERSE}{\mathcal{U}} +\newcommand{\natg}[3]{% + \stackrel[#3]{#2}{\overrightarrow{\underrightarrow{\;{#1}\;}}}} +\newcommand{\nats}[1]{\natg{\downarrow\,{#1}}{}{}} +\newcommand{\nati}[1]{\natg{\cong\,{#1}}{}{}} +\newcommand{\nattwog}[4]{% + \stackrel[#4]{#3}{\overrightarrow{\underrightarrow{% + \xrightarrow[\;{#2}\hfil]{\;{#1}\hfil}}}}} +\newcommand{\nattwos}[2]{\nattwog{\downarrow\,{#1}}{\downarrow\,{#2}}{}{}} +\newcommand{\nattwoi}[2]{\nattwog{\cong\,{#1}}{\cong\,{#2}}{}{}} +\newcommand{\logicrule}[2]{\frac{\displaystyle{#1}}{\displaystyle{#2}}} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/present/fig/monad_data.svg b/present/fig/monad_data.svg new file mode 100644 index 0000000..c232b50 --- /dev/null +++ b/present/fig/monad_data.svg @@ -0,0 +1,72 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/present/fig/monad_data.tex b/present/fig/monad_data.tex new file mode 100644 index 0000000..957e44c --- /dev/null +++ b/present/fig/monad_data.tex @@ -0,0 +1,16 @@ +\documentclass[12pt]{standalone} +\input{head} +\begin{document} +\begin{tikzpicture}\selectlanguage{english} + \path (0,2) node(TTT){$T^3$} (2,2) node(TTP){$T^2$}; + \path (0,0) node(PTT){$T^2$} (2,0) node(T){$T$}; + \draw[->] (TTT) -- node[above]{$T\mu$} (TTP); + \draw[->] (TTT) -- node[left]{$\mu T$}(PTT); + \draw[->] (TTP) -- node[right]{$\mu$} (T); + \draw[->] (PTT) -- node[below]{$\mu$} (T); +\end{tikzpicture} +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/present/fig/monad_data_adj.svg b/present/fig/monad_data_adj.svg new file mode 100644 index 0000000..3b8899f --- /dev/null +++ b/present/fig/monad_data_adj.svg @@ -0,0 +1,118 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/present/fig/monad_data_adj.tex b/present/fig/monad_data_adj.tex new file mode 100644 index 0000000..938e6bf --- /dev/null +++ b/present/fig/monad_data_adj.tex @@ -0,0 +1,16 @@ +\documentclass[12pt]{standalone} +\input{head} +\begin{document} +\begin{tikzpicture}\selectlanguage{english} + \path (0,2) node(TTT){$(GF)^3$} (3,2) node(TTP){$(GF)^2$}; + \path (0,0) node(PTT){$(GF)^2$} (3,0) node(T){$GF$}; + \draw[->] (TTT) -- node[above]{$GFG\varepsilon F$} (TTP); + \draw[->] (TTT) -- node[left]{$G\varepsilon FGF$}(PTT); + \draw[->] (TTP) -- node[right]{$G\varepsilon F$} (T); + \draw[->] (PTT) -- node[below]{$G\varepsilon F$} (T); +\end{tikzpicture} +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/present/fig/monad_data_pow.svg b/present/fig/monad_data_pow.svg new file mode 100644 index 0000000..51f1e9a --- /dev/null +++ b/present/fig/monad_data_pow.svg @@ -0,0 +1,135 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/present/fig/monad_data_pow.tex b/present/fig/monad_data_pow.tex new file mode 100644 index 0000000..d0533e2 --- /dev/null +++ b/present/fig/monad_data_pow.tex @@ -0,0 +1,16 @@ +\documentclass[12pt]{standalone} +\input{head} +\begin{document} +\begin{tikzpicture}\selectlanguage{english} + \path (0,2) node(TTT){$\mathcal{S}$} (2,2) node(TTP){$\{\bigcup S\}_{S\in\mathcal{S}}$}; + \path (0,0) node(PTT){$\bigcup\mathcal{S}$} (2,0) node(T){$\bigcup\bigcup\mathcal{S}$}; + \tikzsquig (TTT) -- node[above]{$\power\mu_X$} (TTP); + \tikzsquig (TTT) -- node[left]{$\mu_{\power X}$}(PTT); + \tikzsquig (TTP) -- node[right]{$\mu_X$} (T); + \tikzsquig (PTT) -- node[below]{$\mu_X$} (T); +\end{tikzpicture} +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/present/fig/monad_unit.svg b/present/fig/monad_unit.svg new file mode 100644 index 0000000..7eba3f3 --- /dev/null +++ b/present/fig/monad_unit.svg @@ -0,0 +1,97 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/present/fig/monad_unit.tex b/present/fig/monad_unit.tex new file mode 100644 index 0000000..f100b66 --- /dev/null +++ b/present/fig/monad_unit.tex @@ -0,0 +1,17 @@ +\documentclass[12pt]{standalone} +\input{head} +\begin{document} +\begin{tikzpicture}\selectlanguage{english} + \path (0,2) node(IT){$1\circ T$} (2,2) node(TT){$T^2$} (4,2) node(TI){$T\circ 1$}; + \path (2,0) node(T){$T$} node[below]{$\phantom{\mu}$}; + \draw[->] (IT) -- node[above]{$\eta T$} (TT); + \draw[->] (TI) -- node[above]{$T\eta$} (TT); + \draw[->] (TT) -- node[right]{$\mu$} (T); + \draw[->] (IT) -- node[left]{$1$} (T); + \draw[->] (TI) -- node[right]{$1$} (T); +\end{tikzpicture} +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/present/fig/monad_unita_adj.svg b/present/fig/monad_unita_adj.svg new file mode 100644 index 0000000..c6c7eef --- /dev/null +++ b/present/fig/monad_unita_adj.svg @@ -0,0 +1,102 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/present/fig/monad_unita_adj.tex b/present/fig/monad_unita_adj.tex new file mode 100644 index 0000000..46d177e --- /dev/null +++ b/present/fig/monad_unita_adj.tex @@ -0,0 +1,17 @@ +\documentclass[12pt]{standalone} +\input{head} +\begin{document} +\begin{tikzpicture}\selectlanguage{english} + \path (0,2) node(IT){$GF$} (2,2) node(TT){$(GF)^2$} (4,2) node(TI){$GF$}; + \path (2,0) node(T){$GF$} node[below]{$\phantom{\mu}$}; + \draw[->] (IT) -- node[above]{$\eta GF$} (TT); + \draw[->] (TI) -- node[above]{$GF\eta$} (TT); + \draw[->] (TT) -- node{$G\varepsilon F$} (T); + \draw[->] (IT) -- node[left]{$1$} (T); + \draw[->] (TI) -- node[right]{$1$} (T); +\end{tikzpicture} +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: \ No newline at end of file diff --git a/present/fig/monad_unita_pow.svg b/present/fig/monad_unita_pow.svg new file mode 100644 index 0000000..f4da587 --- /dev/null +++ b/present/fig/monad_unita_pow.svg @@ -0,0 +1,93 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/present/fig/monad_unita_pow.tex b/present/fig/monad_unita_pow.tex new file mode 100644 index 0000000..d299d54 --- /dev/null +++ b/present/fig/monad_unita_pow.tex @@ -0,0 +1,15 @@ +\documentclass[12pt]{standalone} +\input{head} +\begin{document} +\begin{tikzpicture}\selectlanguage{english} + \path (0,2) node(IT){$S$} (2,2) node(TT){$\{S\}$}; + \path (2,0) node(T){$S$} node[below]{$\phantom{\mu}$}; + \tikzsquig (IT) -- node[above]{$\eta_{\power X}$} (TT); + \tikzsquig (TT) -- node[right]{$\mu_X$} (T); + \tikzsquig (IT) -- node[left]{$1_{\power X}$} (T); +\end{tikzpicture} +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/present/fig/monad_unitb_pow.svg b/present/fig/monad_unitb_pow.svg new file mode 100644 index 0000000..49d729c --- /dev/null +++ b/present/fig/monad_unitb_pow.svg @@ -0,0 +1,119 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/present/fig/monad_unitb_pow.tex b/present/fig/monad_unitb_pow.tex new file mode 100644 index 0000000..884df9f --- /dev/null +++ b/present/fig/monad_unitb_pow.tex @@ -0,0 +1,15 @@ +\documentclass[12pt]{standalone} +\input{head} +\begin{document} +\begin{tikzpicture}\selectlanguage{english} + \path (2,2) node(TT){$\{\{s\}\}_{s\in S}$} (4,2) node(TI){$S$}; + \path (2,0) node(T){$S$} node[below]{$\phantom{\mu}$}; + \tikzsquig (TI) -- node[above]{$\power\eta_X$} (TT); + \tikzsquig (TT) -- node[right]{$\mu_X$} (T); + \tikzsquig (TI) -- node[right]{$1_{\power X}$} (T); +\end{tikzpicture} +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/present/fig/natural.svg b/present/fig/natural.svg new file mode 100644 index 0000000..69bcb0f --- /dev/null +++ b/present/fig/natural.svg @@ -0,0 +1,106 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/present/fig/natural.tex b/present/fig/natural.tex new file mode 100644 index 0000000..90c6597 --- /dev/null +++ b/present/fig/natural.tex @@ -0,0 +1,17 @@ +\documentclass[12pt]{standalone} +\input{head} +\begin{document} +\begin{tikzpicture}\selectlanguage{english} + \path (0,2) node(A){$a$} (2,2) node(SA){$Sa$} (4,2) node(TA){$Ta$}; + \path (0,0) node(B){$b$} (2,0) node(SB){$Sb$} (4,0) node(TB){$Tb$}; + \draw[->] (A) -- node[right]{$f$} (B); + \draw[->] (SA) -- node[left]{$Sf$} (SB); + \draw[->] (TA) -- node[right]{$Tf$} (TB); + \draw[->] (SA) -- node[above]{$\tau_a$} (TA); + \draw[->] (SB) -- node[below]{$\tau_b$} (TB); +\end{tikzpicture} +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/present/fig/universal.svg b/present/fig/universal.svg new file mode 100644 index 0000000..17c1281 --- /dev/null +++ b/present/fig/universal.svg @@ -0,0 +1,86 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/present/fig/universal.tex b/present/fig/universal.tex new file mode 100644 index 0000000..9e5c5d9 --- /dev/null +++ b/present/fig/universal.tex @@ -0,0 +1,16 @@ +\documentclass[12pt]{standalone} +\input{head} +\begin{document} +\begin{tikzpicture}\selectlanguage{english} + \path (0,2) node(B){$b$} (2,2) node(UC){$Uc$} (4,2) node(C){$c$}; + \path (2,0) node(UX){$Ux$} (4,0) node(X){$x$}; + \draw[->] (B) -- node[above]{$u$} (UC); + \draw[->] (B) -- node[left]{$f$} (UX); + \draw[->,dotted] (UC) -- node[right]{$U\hat f$} (UX); + \draw[->,dotted] (C) -- node[right]{$\hat f$} (X); +\end{tikzpicture} +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: -- cgit v1.2.3