5 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…
Categorical-algebraic aspects of Heyting semilattices
Xabier García-Martínez, James R. A. Gray, Michael A. Hoefnagel +2
This article gives an overview of some key categorical-algebraic properties of the variety of Heyting semilattices, with the aim of correcting a misconception in the literature. We…
Non-additive derived functors via chain resolutions
Maxime Culot, Fara Renaud, Tim Van der Linden
Let be a functor from a category to a homological (Borceux-Bourn) or semi-abelian (Janelidze-Márki-Tholen) category $\mathcal{E}…
A Homological View of Categorical Algebra
George Peschke, Tim Van der Linden
We provide a foundation for working with homological and homotopical methods in categorical algebra. This involves two mutually complementary components, namely (a) the strategic s…
Twisted Commutators and Internal Crossed Modules
Bo Shan Deval, Tim Van der Linden
We introduce a notion of relative commutator -- an important special case being commutators twisted by an action -- as a straightforward modification of the definition of the Higgi…