Kernels, lax algebras, d\'ecalage, and supercoherence
Category Theory
2026-02-05 v1 Algebraic Topology
Abstract
We prove that a pointed category has kernels if and only if it is a lax algebra for the arrow 2-monad, and that this holds if and only if it is the d\'ecalage of a supercoherent structure. We will then interpret categories with kernels as the sought-after weak version of unary operadic categories.
Cite
@article{arxiv.2601.20322,
title = {Kernels, lax algebras, d\'ecalage, and supercoherence},
author = {Martin Markl and Dominik Trnka},
journal= {arXiv preprint arXiv:2601.20322},
year = {2026}
}
Comments
34 pages