9 papers
Intrinsic tensor products and a Ganea-type extension of the five-term exact sequence
Bo Shan Deval, Manfred Hartl, Tim Van der Linden
We define an intrinsic symmetric bi-right-exact (and for varieties, bi-cocontinuous) bilinear product on objects of a semi-abelian category, constructed as the cosmash product in t…
Weak action representability of 2-nilpotent groups
Alessandro Dioguardi Burgio, Manuel Mancini, Tim Van der Linden
In this article, we investigate the representability of actions of the category of -nilpotent groups. We first provide an algebraic characterisati…
Homological lemmas for (non-abelian) group-like structures by diagram chasing in a self-dual context
Kishan Kumar Dayaram, Amartya Goswami, Zurab Janelidze +2
Through abelian categories, homological lemmas for modules admit a self-dual treatment, where half of the proof of a lemma is sufficient to prove the full lemma. In this paper, we…
A comparison between weakly protomodular and protomodular objects in unital categories
Xabier GarcÃa-MartÃnez, Andrea Montoli, Diana Rodelo +1
We compare the concepts of protomodular and weakly protomodular objects within the context of unital categories. Our analysis demonstrates that these two notions are generally dist…
From Abelianization to Tangent Categories
Sacha Ikonicoff, Jean-Simon Pacaud Lemay, Tim Van der Linden
A tangent category is a category with an endofunctor, called the tangent bundle functor, which is equipped with various natural transformations that capture essential properties of…
Categorical-algebraic aspects of Heyting semilattices
Xabier GarcÃa-MartÃnez, 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…