Moduli stacks of linear and abelian categories
type: Dataset
description: Linear categories naturally have several identification relations : isomorphisms, categorical equivalences and Morita equivalences. In this thesis, we construct the classifying stacks for these three relations ($\ukcatiso$, $\ukcateq$, $\ukcatmor$) together with the classifying stack of abelian categories ($\ukab$), the originality of the subject being that, apart from the first one, these are higher stacks. The principal result is that, under some finiteness assumptions, these stacks are geometric in the sense of C.~Simpson. In particular, one recover the Hochschild cohomology of a category $C$ as the tangent complex, i.e. the object classifying first order deformations of $C$, of these stacks at the point defined by $C$. Moreover, there exists a natural sequence of surjective morphisms of stacks : $$\ukcatiso \tto \ukcateq \tto \ukcatmor \tto \ukab$$ for which we prove that the middle one is etale, and the right one is an equivalence.
landing page: https://theses.hal.science/tel-00085627
keyword: abelian-categories
keyword: categories-abeliennes
keyword: champs-superieurs
keyword: cohomologie-de-hochschild
keyword: complexe-tangent
keyword: higher-stacks
keyword: hochschild-cohomology
keyword: infoeu-reposemanticsdoctoralthesis
keyword: mathmathematics-math
keyword: tangent-complex
keyword: theses
issued: 2026-05-09T22:54:48.358174
modified: 2026-05-09T22:54:48.358179
language: fr
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Moduli stacks of linear and abelian categories
type: Distribution
format: HTML
access URL: https://theses.hal.science/tel-00085627
issued: 2026-05-09T22:54:48.362496
modified: 2026-05-09T22:54:48.346892