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arXiv · 2604.05744

On the decomposition of a strong epimorphism into regular epimorphisms

Yuto Kawase·Hayato Nasu
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Abstract

Strong epimorphisms and regular epimorphisms are two important classes of morphisms, and they do not coincide in general. Yet, in a locally presentable category, it is known that any strong epimorphism can be decomposed into a transfinite composite of regular epimorphisms. In this paper, we provide two syntactic methods to determine how many regular epimorphisms are needed in such a decomposition, using partial Horn theory and generalized algebraic theory. We start by discussing a general problem of decomposing a morphism into a transfinite composite of morphisms in a given class, which also covers the decomposition of an adjoint functor into monadic functors.

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Yuto Kawase, Hayato Nasu. 2026-04-07. On the decomposition of a strong epimorphism into regular epimorphisms. https://arxiv.org/abs/2604.05744

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