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arXiv · 2603.06355

The five-sequence of adjoints for combinatorial simplicial complexes

Gunnar Fløystad
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Abstract

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.

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Gunnar Fløystad. 2026-03-06. The five-sequence of adjoints for combinatorial simplicial complexes. https://arxiv.org/abs/2603.06355

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