English

Module des diff{\'e}rentielles

Category Theory 2023-04-12 v1

Abstract

For any object x in a category C it is possible to define the category of Beck modules over x as the category Ab(C/x) of abelian group objects in the category C/x. We can deduce from this construction, at least for any locally presentable category, the notion of cotangent module or module of differentials Ω\Omegax of x in Ab(C/x).In the case of the category Algk of commutative k-algebras over a ring k, the category of Beck modules Ab(Algk/A) over a k-algebra A is equivalent to the category ModA of A-modules and the cotangent module is equal to the module of K{\"a}hler differentials of A.The aim of this article is to prove for any locally presentable category some results which generalize the classical properties of modules of K{\"a}hler differentials.

Keywords

Cite

@article{arxiv.2304.05101,
  title  = {Module des diff{\'e}rentielles},
  author = {Michel Vaquié},
  journal= {arXiv preprint arXiv:2304.05101},
  year   = {2023}
}

Comments

in French language

R2 v1 2026-06-28T09:59:16.908Z