Coherence for adjunctions in a $4$-category
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910679073554432 |
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| author | Araújo, Manuel |
| author_facet | Araújo, Manuel |
| contents | We give a definition of a coherent adjunction in a $4$-category consisting of a finite list of $k$-morphisms for $k\leq 4$, plus equations beetween $4$-morphisms. We prove that the restriction map from the space of coherent adjunctions in a $4$-category to the space of $1$-morphisms which admit an adjoint is a trivial fibration. We prove that other restriction maps related to fixing parts of the data of an adjunction are also trivial fibrations. We give a conjectural description of a coherent adjunction in an $n$-category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_02935 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Coherence for adjunctions in a $4$-category Araújo, Manuel Category Theory Quantum Algebra We give a definition of a coherent adjunction in a $4$-category consisting of a finite list of $k$-morphisms for $k\leq 4$, plus equations beetween $4$-morphisms. We prove that the restriction map from the space of coherent adjunctions in a $4$-category to the space of $1$-morphisms which admit an adjoint is a trivial fibration. We prove that other restriction maps related to fixing parts of the data of an adjunction are also trivial fibrations. We give a conjectural description of a coherent adjunction in an $n$-category. |
| title | Coherence for adjunctions in a $4$-category |
| topic | Category Theory Quantum Algebra |
| url | https://arxiv.org/abs/2207.02935 |