4 papers
R-full Schreier internal categories and their directions
Stefano Ambra, Andrea Montoli, Diana Rodelo
We introduce the notion of R-full Schreier internal category, which is the monoid analogue of the notion of aspherical abelian groupoid. We associate with every R-full Schreier int…
A direction functor approach to the cohomology of small categories
Stefano Ambra, Arnaud Duvieusart, Andrea Montoli
We show how the direction functors can be used to develop a cohomology theory for Barr-exact and S-Maltsev categories, where S is a suitable class of split epimorphisms with a fixe…
Actions, semidirect products and crossed semimodules in the category of small categories with a fixed set of objects
Stefano Ambra
We generalize to the fibres of the fibration defined by mapping a small category to its set of objects $X_0=ob(…
The direction functor for Schreier extensions of monoids
Stefano Ambra, Andrea Montoli, Diana Rodelo
We observe that the process of associating an action to any Schreier extension of monoids with commutative and cancellative kernel is functorial. We show that this functor is a gen…