Ternary structures and groupoids
The category of groupoid graded modules
We introduce the abelian category R-gr of groupoid graded modules and give an answer to the following general question: If U: R-gr → R-mod denotes the functor which associates to any graded left R-module M the underlying ungraded structure U(M), when does either of the following two implications hold: (I) M has property X ⇒ U(M) has property X; (II) U(M) has property X ⇒ M has property X? We treat the cases when X is one of the properties: direct summand, free, finitely generated, finitely presented,...
The classifying topos of a continuous groupoid. II
The connection between the fundamental groupoid and a unification algorithm for syntactil algebras (extended abstract)
The low-dimensional homology of crossed modules.
The Mal'tsev operation on extensions
The shift functor and the comprehensive factorization for internal groupoids
The stack quotient of a groupoid