A comparison between weakly protomodular and protomodular objects in unital categories
Category Theory
2025-11-11 v2
Abstract
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 distinct. To establish this, we introduce left pseudocancellative unital magmas and characterise weakly protomodular objects within the variety of algebras they constitute. Subsequently, we present an example of a weakly protomodular object that is not protomodular in this category.
Keywords
Cite
@article{arxiv.2409.19076,
title = {A comparison between weakly protomodular and protomodular objects in unital categories},
author = {Xabier García-Martínez and Andrea Montoli and Diana Rodelo and Tim Van der Linden},
journal= {arXiv preprint arXiv:2409.19076},
year = {2025}
}
Comments
10 pages; extended proofs and examples