Searcharxiv⌕ Search

arXiv · 2610.25198

Finitely enhanced nontopological triangulated categories

Abstract

Over every nonzero commutative ring $R$, we construct a nontopological triangulated category over $R$, whose finitely generated thick subcategories are alegbraic, while the scalar action of $R$ is faithful.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Chencheng Zhang. 2026-10-18. Finitely enhanced nontopological triangulated categories. https://arxiv.org/abs/2610.25198

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

A skew approach to enrichment for Gray-categories

It is well known that the category of Gray-categories does not admit a monoidal biclosed structure that models weak higher-dimensional transformations. In this paper, the first of a series on the topic, we describe several skew monoidal closed structures on the category of Gray-categories, one of which captures higher lax transformations, and another which models higher pseudo-transformations.

math.CT↗

Enriched positive logic

Building on our previous work on enriched regular logic, we introduce an enriched version of positive logic and relate it to enriched cone-injectivity classes and enriched accessible categories. To do this, we need a factorization system on the base of enrichment in order to interpret existential quantification and disjunctions. We will also show how to treat unique existence in enriched logic, and how to relate it to local presentability.

math.CT↗

Simple-shifted monoidal derived equivalences for tensor categories

In this paper, we investigate monoidal derived equivalences between tensor categories with infinitely many isomorphism classes of simple objects. We introduce the notion of a simple-shifted monoidal derived equivalence and prove that a simple-shifted monoidal derived equivalence gives rise to a tensor equivalence. In addition, we investigate which tensor categories have the property that every monoidal derived equivalence between them is necessarily simple-shifted, and we establish some sufficient conditions for this property. As a corollary, we show that a monoidal derived equivalence between pointed tensor categories implies a tensor equivalence between them.

math.CT↗