On the decomposition of a strong epimorphism into regular epimorphisms
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915920600891392 |
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| author | Kawase, Yuto Nasu, Hayato |
| author_facet | Kawase, Yuto Nasu, Hayato |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05744 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the decomposition of a strong epimorphism into regular epimorphisms Kawase, Yuto Nasu, Hayato Category Theory 18A20, 18A32, 18C10, 18C35 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. |
| title | On the decomposition of a strong epimorphism into regular epimorphisms |
| topic | Category Theory 18A20, 18A32, 18C10, 18C35 |
| url | https://arxiv.org/abs/2604.05744 |