contents/category_theory.tex : Added homomorphism definition and useful macros

packages/macros.sty

@@ -19,17 +19,23 @@
 \newcommand{\C}{\mathbb{C}}			% Complex numbers symbol
 \newcommand{\Cat}{\mathcal{C}}			% Category
 \newcommand{\Set}{\mathbf{Set}}			% Set category
+\newcommand{\Grp}{\mathbf{Grp}}			% Group category
+\newcommand{\Ab}{\mathbf{Ab}}			% Abelian category
+\newcommand{\Top}{\mathbf{Top}}			% Topological spaces category
 \newcommand{\K}{\mathbb{K}}			% Corps
 \newcommand{\Hq}{\mathbb{H}}			% Quaternions numbers symbol
 \newcommand{\Ot}{\mathbb{O}}			% Octonions numbers symbol
 \newcommand{\Se}{\mathbb{S}}			% Sedenions numbers symbol
 \newcommand{\Pn}{\mathbb{P}}			% Sets of all the prime numbers
 \newcommand{\B}{\mathbf{B}}			% Topological Ball
+\newcommand{\Identity}{\text{Id}}		% Identity
+\newcommand{\identity}{\text{id}}		% identity
 \newcommand{\false}{F}				% New symbol for false value
 \newcommand{\true}{V}				% New symbol for true value
 \DeclareMathOperator{\Rel}{\mathcal{R}}		% New symbol for binary relations
 \DeclareMathOperator{\composes}{\circ}		% New symbol composing morphisms
 \DeclarePairedDelimiter{\abs}{|}{|}
+\newcommand{\isomorphic}{\cong}			% Isomorphism
 \DeclarePairedDelimiter{\card}{|}{|}
 \DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor}
 \DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}