Add \unit{} for the multiplicative identity element.

Technically we could pass off \identity{X} as the multiplicative
identity element in an algebraic structure, by using the "arrow"
interpretation in the right category. But let's not try to shoot
ourselves in the foot too hard, yeah?

diff --git a/examples.tex b/examples.tex
index 131a213b5a465894f7691edf546952e676c2e8b1..65e0c80b69f960cb07f1e2790c61eb12e6b1e911 100644 (file)
--- a/examples.tex
+++ b/examples.tex
@@ -36,6 +36,9 @@
     $\mathcal{A}$ and if $x,y,z \in \mathcal{A}$, then
     $\alg{\set{x,y,z}}$ is the smallest subalgebra of $\mathcal{A}$
     containing the set $\set{x,y,z}$.
+
+    If $R$ has a multiplicative identity (that is, a unit) element,
+    then that element is denoted by $\unit{R}$.
   \end{section}
 
   \begin{section}{Algorithm}

diff --git a/mjo-algebra.tex b/mjo-algebra.tex
index 7ff7b5ae737ac2c14cbe4eda7af0a4f72fde2a5d..36ad4bd64888c1b2926ff2d454c989e3a561a6aa 100644 (file)
--- a/mjo-algebra.tex
+++ b/mjo-algebra.tex
@@ -12,6 +12,18 @@
 \input{mjo-common} % for \of, and \binopmany
 
 
+% The multiplicative identity element of its argument, which should be
+% an algebraic structure.
+\newcommand*{\unit}[1]{ 1_{{#1}} }
+
+\ifdefined\newglossaryentry
+  \newglossaryentry{unit}{
+    name={\ensuremath{\unit{R}}},
+    description={the multiplicative identity (unit) element of $R$},
+    sort=u
+  }
+\fi
+
 % The direct sum of two things.
 \newcommand*{\directsum}[2]{ {#1}\oplus{#2} }
 

diff --git a/mjo-arrow.tex b/mjo-arrow.tex
index 9bf9dc5555515e45f2a98b25d5c89310375d3b03..2d5095ee327b9866bbd84b8098f8d7a084bd27f7 100644 (file)
--- a/mjo-arrow.tex
+++ b/mjo-arrow.tex
@@ -23,9 +23,17 @@
   }
 \fi
 
-% The identity operator/arrow on its argument.
+% The identity function/arrow on its argument.
 \newcommand*{\identity}[1]{ \operatorname{id}_{{#1}} }
 
+\ifdefined\newglossaryentry
+  \newglossaryentry{identity}{
+    name={\ensuremath{\identity{X}}},
+    description={the identity function or arrow on $X$},
+    sort=i
+  }
+\fi
+
 % The composition of two arrows/functions. For example, the
 % composition of g with f is \compose{g}{f}\of{x} === g\of{f\of{x}}.
 \newcommand*{\compose}[2]{ {#1}\circ{#2} }