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<record version="7" id="1691">
 <title>groupoid</title>
 <name>Groupoid</name>
 <created>2002-02-02 22:46:02</created>
 <modified>2002-11-06 19:19:28</modified>
 <type>Definition</type>
 <creator id="2" name="akrowne"/>
 <author id="2" name="akrowne"/>
 <classification>
	<category scheme="msc" code="20N02"/>
 </classification>
 <synonyms>
	<synonym concept="groupoid" alias="magma"/>
 </synonyms>
 <related>
	<object name="Semigroup"/>
	<object name="Group"/>
	<object name="LoopAndQuasigroup"/>
 </related>
 <preamble>\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}

%\usepackage{psfrag}
%\usepackage{graphicx}
%\usepackage{xypic}</preamble>
 <content>A groupoid $G$ is a set together with a binary operation $\cdot : G \times G \longrightarrow G$.  The groupoid (or ``magma'') is closed under the operation.

There is also a separate, \PMlinkname{category-theoretic}{GroupoidCategoryTheoretic} definition of ``groupoid.''</content>
</record>
