Kernels, lax algebras, d\'ecalage, 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 d\'ecalage of a supercoherent structure. We will then interpret categories with kernels as the sought-after weak version of unary operadic categories.
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