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arXiv · 1505.07086

Cartesian modules over representations of small categories

Sergio Estrada·Simone Virili
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Abstract

We introduce the new concept of cartesian module over a pseudofunctor $R$ from a small category to the category of small preadditive categories. Already the case when $R$ 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.

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Sergio Estrada, Simone Virili. 2015-05-26. Cartesian modules over representations of small categories. https://arxiv.org/abs/1505.07086

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