Kernels, lax algebras, décalage, and supercoherence
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 décalage of a supercoherent structure. We will then interpret categories with kernels as the sought-after weak version of unary operadic categories.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Logic
programming
and type systems
Advanced Algebra and Logic
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 28 January 2026
- Language
- EN
- Document type
- Preprint