Lax Additivity
Category Theory
2025-11-18 v2 Algebraic Topology
Abstract
We introduce notions of lax semiadditive and lax additive -categories, categorifying the classical notions of semiadditive and additive 1-categories. To establish a well-behaved axiomatic framework, we develop a calculus of lax matrices and use it to prove that in locally cocomplete -categories lax limits and lax colimits agree and are absolute. In the lax additive setting, we categorify fundamental constructions from homological algebra such as mapping complexes and mapping cones and establish their basic properties.
Cite
@article{arxiv.2402.12251,
title = {Lax Additivity},
author = {Merlin Christ and Tobias Dyckerhoff and Tashi Walde},
journal= {arXiv preprint arXiv:2402.12251},
year = {2025}
}
Comments
62 pages. Companion paper to arXiv:2301.02606. v2: added short appendix on recollements; to appear in Documenta Mathematica