Cartesian modules over representations of small categories
Rings and Algebras
2015-05-27 v1 Algebraic Geometry
Algebraic Topology
Category Theory
Abstract
We introduce the new concept of cartesian module over a pseudofunctor from a small category to the category of small preadditive categories. Already the case when is a (strict) functor taking values in the category of commutative rings is sufficient to cover the classical construction of quasi-coherent sheaves of modules over a scheme. On the other hand, our general setting allows for a good theory of contravariant additive locally flat functors, providing a geometrically meaningful extension of Crawley-Boevey's Representation Theorem. As an application, we relate and extend some previous constructions of the pure derived category of a scheme.
Cite
@article{arxiv.1505.07086,
title = {Cartesian modules over representations of small categories},
author = {Sergio Estrada and Simone Virili},
journal= {arXiv preprint arXiv:1505.07086},
year = {2015}
}