The five-sequence of adjoints for combinatorial simplicial complexes
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915839681232896 |
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| author | Fløystad, Gunnar |
| author_facet | Fløystad, Gunnar |
| contents | For a set $A$ let ${\mathbf {SC}_A}$ be the poset of simplicial complexes whose vertices are in $A$. For a function $f : A \rightarrow B$ there are functors $ f^{! !}, f^{**}, f^{ii}: {\mathbf {SC}_A} \rightarrow {\mathbf {SC}_B}, \quad f^{!*}, f^{i*} : {\mathbf {SC}_B} \rightarrow {\mathbf {SC}_A}, $ forming a five sequence of adjoints $f^{ !!} \dashv f^{* !} \dashv f^{* *} \dashv f^{*i} \dashv f^{ii}$.
We investigate in detail these functors, and use this to give three categorical structures on simplicial complexes on finite sets such that the Stanley-Reisner correspondence to commutative monomial rings gives dualities. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_06355 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The five-sequence of adjoints for combinatorial simplicial complexes Fløystad, Gunnar Combinatorics Commutative Algebra Category Theory Primary: 05E45, 18B35, Secondary: 13F55 For a set $A$ let ${\mathbf {SC}_A}$ be the poset of simplicial complexes whose vertices are in $A$. For a function $f : A \rightarrow B$ there are functors $ f^{! !}, f^{**}, f^{ii}: {\mathbf {SC}_A} \rightarrow {\mathbf {SC}_B}, \quad f^{!*}, f^{i*} : {\mathbf {SC}_B} \rightarrow {\mathbf {SC}_A}, $ forming a five sequence of adjoints $f^{ !!} \dashv f^{* !} \dashv f^{* *} \dashv f^{*i} \dashv f^{ii}$. We investigate in detail these functors, and use this to give three categorical structures on simplicial complexes on finite sets such that the Stanley-Reisner correspondence to commutative monomial rings gives dualities. |
| title | The five-sequence of adjoints for combinatorial simplicial complexes |
| topic | Combinatorics Commutative Algebra Category Theory Primary: 05E45, 18B35, Secondary: 13F55 |
| url | https://arxiv.org/abs/2603.06355 |