Internal categories and groupoids in congruence modular varieties (Q1364303)

The so-called `congruence modular varieties' are the algebraic categories in the sense of Lawvere in which the congruences, i.e., the equivalence relations which are compatible with the operations, satisfy the modular identity. The paper shows that, in these categories, there is a connection between internal category theory and commutator theory introduced in universal algebra. It describes all internal categories satisfying a certain commutator condition which always holds for internal groupoids and for all internal categories in Mal'tsev varieties.