Equivariant closure operators and trisp closure maps

TL;DR

This paper explores the properties of trisp closure maps, their interaction with group actions, and their relationship with closure operators on posets, providing new insights into their structural behavior.

Contribution

It introduces conditions under which quotient maps preserve trisp closure maps and links these maps to closure operators on posets, especially for nerves of acyclic categories.

Findings

Quotient maps can be trisp closure maps under specific conditions.

Trisp closure maps relate closely to closure operators on posets.

The study enhances understanding of the structure of nerves of acyclic categories.

Abstract

A trisp closure map is a special map on the vertices of a trisp T with the property that T collapses onto the subtrisp induced by the image of the map. We study the interaction between trisp closure maps and group operations on the trisp, and give conditions such that the quotient map is again a trisp closure map. Special attention is on the case that the trisp is the nerve of an acyclic category, and the relationship between trisp closure maps and closure operators on posets is studied.