Year: 2025
Type: article
Abstract: Let $$\mathbf{C}$$ be a small category. The subtoposes of $$[\mathbf{C}^\textrm{op},\mathbf{Set}]$$ are sometimes all of the form $$[\mathbf{D}^\textrm{op},\mathbf{Set}]$$ where $$\mathbf{D}$$ is a full subcategory of $$\mathbf{C}$$ . This is the case for instance when $$\mathbf{C}$$ is Cauchy-complete and finite, an Artinian poset, or the simplex category. We call such a category universally rigid . A universally rigid category whose slices are also universally rigid, such as the aforementioned examples, is called stably universally rigid . We provide two equivalent characterizations of such categories. The first one stipulates the existence of a winning strategy in a two-player game, and the second one combines two “local” properties of $$\mathbf{C}$$ involving respectively the poset reflections of its slices and its endomorphism monoids.
Source: Applied Categorical Structures
Author: Jérémie Marquès
Institution: University of Milan
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Awards: G1686424, G199127864, G434337789
OpenAlex ID: W4415300644