Mal’tsev and Lawvere functors

Abstract

We investigate, at the level of functors, the effect of definitions mimicking those of Mal’tsev and naturally Mal’tsev categories, and show that they give rise to the same kind of characterizations. We give, among others, an application concerning the characterization of the Smith=Huq condition.

Mathematics Subject Classification (2010):

• 08B10
• 08C05
• 18A20
• 18A32
• 18E13

Key words:

• Internal groupoids
• Mal’tsev
• naturally Mal’tsev and protomodular categories
• Σ-Mal’tsev categories
• centralization of equivalence relations
• Smith=Huq condition