diff options
| -rw-r--r-- | default.nix | 2 | ||||
| -rw-r--r-- | provider/posts/simmons-intro-to-cat-t/1.1.md | 12 | ||||
| -rw-r--r-- | tex/preamble.tex | 7 | 
3 files changed, 14 insertions, 7 deletions
diff --git a/default.nix b/default.nix index d6e481e..0770eb3 100644 --- a/default.nix +++ b/default.nix  | |||
| @@ -11,7 +11,7 @@ rec { | |||
| 11 | } | 11 | } | 
| 12 | ); | 12 | ); | 
| 13 | texEnv = with pkgs; texlive.combine { | 13 | texEnv = with pkgs; texlive.combine { | 
| 14 | inherit (texlive) scheme-small standalone dvisvgm amsmath; | 14 | inherit (texlive) scheme-small standalone dvisvgm amsmath tikz tikz-cd; | 
| 15 | }; | 15 | }; | 
| 16 | dirty-haskell-wrapper = pkgs.stdenv.mkDerivation rec { | 16 | dirty-haskell-wrapper = pkgs.stdenv.mkDerivation rec { | 
| 17 | name = "dirty-haskell-wrapper"; | 17 | name = "dirty-haskell-wrapper"; | 
diff --git a/provider/posts/simmons-intro-to-cat-t/1.1.md b/provider/posts/simmons-intro-to-cat-t/1.1.md index 41aef99..f95c068 100644 --- a/provider/posts/simmons-intro-to-cat-t/1.1.md +++ b/provider/posts/simmons-intro-to-cat-t/1.1.md  | |||
| @@ -10,8 +10,8 @@ Sets and functions do form a category $\ca{Set}$. | |||
| 10 | <div class="proof"> | 10 | <div class="proof"> | 
| 11 | The objects of $\ca{Set}$ are sets and its arrows are functions. | 11 | The objects of $\ca{Set}$ are sets and its arrows are functions. | 
| 12 | 12 | ||
| 13 | For any set $A$ we construct $id_A$ by restricting $id$ to $A$: | 13 | For any set $A$ we construct \idarr{A} by restricting \id to $A$: | 
| 14 | $$id_A = id \upharpoonright A$$ | 14 | $$\idarr{A} = \id \upharpoonright A$$ | 
| 15 | 15 | ||
| 16 | $\circ$ is indeed associative. | 16 | $\circ$ is indeed associative. | 
| 17 | </div> | 17 | </div> | 
| @@ -21,9 +21,9 @@ $\circ$ is indeed associative. | |||
| 21 | Each [poset](https://en.wikipedia.org/wiki/Partially_ordered_set) is a category. | 21 | Each [poset](https://en.wikipedia.org/wiki/Partially_ordered_set) is a category. | 
| 22 | 22 | ||
| 23 | <div class="proof"> | 23 | <div class="proof"> | 
| 24 | The objects of each poset are its elements and we construct an arrow $\leq: a \to b$ for every pair of objects $(a, b)$ iff $a \leq b$. | 24 | The objects of each poset are its elements and we construct an arrow $\begin{tikzcd} a \arrow[r, "\leq"] & b \end{tikzcd}$ for every pair of objects $(a, b)$ iff $a \leq b$. | 
| 25 | 25 | ||
| 26 | Reflexivity ($a \leq a$) and transitivity ($a \leq b \land b \leq c \implies a \leq c$) provide a construction for $id_a$ and $\circ$, respectively. | 26 | Reflexivity ($a \leq a$) and transitivity ($a \leq b \land b \leq c \implies a \leq c$) provide a construction for \idarr{a} and $\circ$, respectively. | 
| 27 | </div> | 27 | </div> | 
| 28 | </div> | 28 | </div> | 
| 29 | 29 | ||
| @@ -31,8 +31,8 @@ Reflexivity ($a \leq a$) and transitivity ($a \leq b \land b \leq c \implies a \ | |||
| 31 | Each [monoid](https://en.wikipedia.org/wiki/Monoid) is a category. | 31 | Each [monoid](https://en.wikipedia.org/wiki/Monoid) is a category. | 
| 32 | 32 | ||
| 33 | <div class="proof"> | 33 | <div class="proof"> | 
| 34 | The objects of each monoid are its elements and we construct for every pair of elements $(a, b)$ an arrow $\cdot b : a \to a \cdot b$. | 34 | The objects of each monoid are its elements and we construct for every pair of elements $(a, b)$ an arrow $\begin{tikzcd} a \arrow[r, "\cdot b"] & a \cdot b \end{tikzcd}$. | 
| 35 | 35 | ||
| 36 | The existence of an identity element and associativity, as required by the monoid structure, immediately provide us with a construction for $id$ and associativity of $\circ$. | 36 | The existence of an identity element and associativity, as required by the monoid structure, immediately provide us with a construction for \id and associativity of $\circ$. | 
| 37 | </div> | 37 | </div> | 
| 38 | </div> | 38 | </div> | 
diff --git a/tex/preamble.tex b/tex/preamble.tex index a583a3b..8ff41d1 100644 --- a/tex/preamble.tex +++ b/tex/preamble.tex  | |||
| @@ -5,5 +5,12 @@ | |||
| 5 | \usepackage{amsmath} | 5 | \usepackage{amsmath} | 
| 6 | \usepackage{mathrsfs} | 6 | \usepackage{mathrsfs} | 
| 7 | 7 | ||
| 8 | \usepackage{tikz} | ||
| 9 | |||
| 10 | \usetikzlibrary{cd} | ||
| 11 | |||
| 8 | \newcommand*{\ca}[1]{\ensuremath{\mathbf{#1}}\xspace} | 12 | \newcommand*{\ca}[1]{\ensuremath{\mathbf{#1}}\xspace} | 
| 13 | \newcommand*{\idarr}[1]{\ensuremath{\mathrm{id}_{#1}}} | ||
| 14 | |||
| 15 | \newcommand{\id}{\ensuremath{\mathrm{id}}} | ||
| 9 | \renewcommand{\implies}{\rightarrow} | 16 | \renewcommand{\implies}{\rightarrow} | 
