6533b7d3fe1ef96bd1260cad

RESEARCH PRODUCT

A note on strong protomodularity, actions and quotients

Giuseppe Metere

subject

Pure mathematicsAlgebra and Number Theory010102 general mathematicsObject (grammar)FibrationMathematics - Category Theory0102 computer and information sciencesCharacterization (mathematics)01 natural sciencesSettore MAT/02 - AlgebraAction (philosophy)010201 computation theory & mathematicsMathematics::Category TheoryFOS: MathematicsOrder (group theory)Category Theory (math.CT)0101 mathematicsQuotientMathematics

description

Abstract In order to study the problems of extending an action along a quotient of the acted object and along a quotient of the acting object, we investigate some properties of the fibration of points. In fact, we obtain a characterization of protomodular categories among quasi-pointed regular ones, and, in the semi-abelian case, a characterization of strong protomodular categories. Eventually, we return to the initial questions by stating the results in terms of internal actions.

yearjournalcountryeditionlanguage
2013-06-17
https://dx.doi.org/10.48550/arxiv.1306.3773