A brief review of abelian categorifications.
A classification of degree functors, I
A classification of degree functors, II
A generalized duality theorem for structure functors
A note on discrete Conduché fibrations.
Abstract initiality
We study morphisms that are initial w.r.t. all functors in a given conglomerate. Several results and counterexamples are obtained concerning the relation of such properties to different notions of subobject. E.g., strong monomorphisms are initial w.r.t. all faithful adjoint functors, but not necessarily w.r.t. all faithful monomorphism-preserving functors; morphisms that are initial w.r.t. all faithful monomorphism-preserving functors are monomorphisms, but need not be extremal; and (under weak...
Accessible set functors are universal
It is shown that every concretizable category can be fully embedded into the category of accessible set functors and natural transformations.
Addendum to completion and closure