Revision as of 00:24, 11 May 2012 edit Purfideas (talk \| contribs) 66 edits →Definition: Adding definition of homomorphism ← Previous edit		Revision as of 01:00, 11 May 2012 edit undo Purfideas (talk \| contribs) 66 edits →Category-theoretic remarks: remark that morphism in the category is a homomorphism and some clarification about M vs Omega Next edit →
Line 20: == Category-theoretic remarks == In [[category theory]], a '''group with operators''' can be defined as an object of a [[functor category]] '''Grp'''<sup>'''M'''</sup> where '''M''' is a monoid (''i.e.'', a category with one object) and '''Grp''' denotes the [[category of groups]]. This definition is equivalent to the previous one, provided <math>\Omega</math> is a monoid (otherwise we may expand it to include the identity and all compositions). A [[morphism]] in this category is a [[natural transformation]] between two functors (''i.e.'' two groups with operators sharing same operator ___domain ''M''). Again we recover the definition above of a homomorphism of groups with operators (with ''f'' the [[Natural_Transformation#Definition\|component]] of the natural transformation). A group with operators is also a mapping

Group with operators: Difference between revisions