10 papers · 1 filter
A two-categorical Snake Lemma
Elena Caviglia, Luca Mesiti, Tim Van der Linden
We prove a Snake Lemma for 2-categories. Working in a 2-category with a strong bizero object, we develop 2-kernels and 2-cokernels, 2-monomorphisms and 2-epimorphisms as fully fait…
Exactness of the 2-categories of abelian and triangulated categories
Elena Caviglia, Zurab Janelidze, Luca Mesiti +1
We introduce a notion of -homological category modelled on pointed homological categories in the sense of Grandis, using bizero objects whose null -cells are zero objects in…
Clifford semigroups and the monoidal Grothendieck construction
Elena Caviglia, Peter F. Faul, Graham Manuell +1
We show that the monoidal Grothendieck construction can be applied to recover the known structure theorem for Clifford monoids, which states that they correspond to functors from a…
Generalized action monads and descent
Elena Caviglia, Sophie Marques, Luca Mesiti
We develop a monadic approach to actions of internal categories. Given an internal category, we construct a monad on a slice whose algebras are the actions of that internal categor…
Comonadic approach to pretorsion theories
Elena Caviglia, Zurab Janelidze, Luca Mesiti
We present a comonadic approach to pretorsion theories on semiexact categories, i.e. categories equipped with a closed ideal of null morphisms that admits all kernels and all coker…
Double Orthogonal Factorization Systems
C. B. Aberlé, Elena Caviglia, Matthew Kukla +4
We define strict and lax orthogonal factorization systems on double categories. These consist of an orthogonal factorization system on arrows and one on double cells that are compa…