INTERNAL CROSSED MODULES AND PEIFFER CONDITION

Giuseppe Metere, Giuseppe Metere, Sandra Mantovani

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)

Abstract

In this paper we show that in a homological category in the sense of F. Borceux and D. Bourn, the notion of an internal precrossed module corresponding to a star-multiplicative graph, in the sense of G. Janelidze, can be obtained by directly internalizing the usual axioms of a crossed module, via equivariance. We then exhibit some sufficient conditions on a homological category under which this notion coincides with the notion of an internal crossed module due to G. Janelidze. We show that this is the case for any category of distributive Omega(2)-groups, in particular for the categories of groups with operations in the sense of G. Orzech.
Original languageEnglish
Pages (from-to)113-135
Number of pages23
JournalTheory and Applications of Categories
Volume23
Publication statusPublished - 2010

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

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