Kernels, lax algebras, décalage, and supercoherence
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910010859061248 |
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| author | Markl, Martin Trnka, Dominik |
| author_facet | Markl, Martin Trnka, Dominik |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20322 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Kernels, lax algebras, décalage, and supercoherence Markl, Martin Trnka, Dominik Category Theory Algebraic Topology 18C15, 18N50, 18M60 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. |
| title | Kernels, lax algebras, décalage, and supercoherence |
| topic | Category Theory Algebraic Topology 18C15, 18N50, 18M60 |
| url | https://arxiv.org/abs/2601.20322 |