Testwiki:Reference desk/Archives/Mathematics/2014 April 14

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April 14

Magma, or groupoid, (algebra)

What is the "normal supgroupoid"? — Preceding unsigned comment added by Amr Jbour (talk • contribs) 17:17, 14 April 2014 (UTC)

A groupoid is an analog of a group in category theory: it is a small category where every morphism has an inverse. A normal subgroupoid is an analog of a normal subgroup: if G is a groupoid, then a normal subgroupoid N has the same set of objects as G and for every morphism f in G, $fN(x,x)f^{-1}=N(x,x)$, where $N(x,x)$ is the set of morphisms from x to itself in N [1]. Then also in analogy to group theory, given G and N, one can form the quotient groupoid G/N, etc. --Mark viking (talk) 17:36, 15 April 2014 (UTC)

 I mean an algebraic structure with one binary operation defined on it, which is closed.

See http://en.wikipedia.org/wiki/Magma_(algebra) 20:14, 16 April 2014 (UTC) --Amr Jbour (talk)--Amr Jbour (talk) 20:34, 16 April 2014 (UTC)

As noted in Groupoid#Comparing the definitions, the algebraic and category-theoretic defns are equivalent. --Mark viking (talk) 22:29, 16 April 2014 (UTC)

I think by "groupoid", the original poster means what is usually called a magma. Magma (algebra) indicates that these are sometimes called "groupoids", but that is actually something different than what is usually meant by "groupoid". You might call a submagma "normal" if every left coset is also a right coset, although I'm not sure if there is a standard use in the literature. Sławomir Biały (talk) 00:14, 17 April 2014 (UTC)