Elmendorf constructions for $G$-categories and $G$-posets

TL;DR

This paper presents new, concrete Elmendorf constructions for equivariant categories and posets, aligning with classical topological methods and providing fresh proofs of Elmendorf theorems in these contexts.

Contribution

It introduces more explicit Elmendorf constructions for equivariant categories and posets, improving upon existing model-categorical approaches.

Findings

Constructions are compatible with classical topological Elmendorf constructions.

New proofs of Elmendorf theorems for equivariant categories and posets.

Constructions are more concrete than previous model-categorical methods.

Abstract

We introduce new Elmendorf constructions for equivariant categories and posets, and we prove that they are compatible with the classical topological one. Our constructions are more concrete than their model-categorical counterparts, and they give rise to new proofs of the Elmendorf theorems for equivariant categories and posets.