Elsevier

Journal of Algebra

Volume 399, 1 February 2014, Pages 675-692
Journal of Algebra

Tensor functors between categories of quasi-coherent sheaves

https://doi.org/10.1016/j.jalgebra.2013.09.050Get rights and content
Under an Elsevier user license
open archive

Abstract

For a quasi-compact quasi-separated scheme X and an arbitrary scheme Y we show that the pullback construction ff implements an equivalence between the discrete category of morphisms YX and the category of cocontinuous tensor functors Qcoh(X)Qcoh(Y). This is an improvement of a result by Lurie and may be interpreted as the statement that algebraic geometry is 2-affine. Moreover, we prove the analogous version of this result for Durovʼs notion of generalized schemes.

MSC

14A15
18D10

Keywords

Quasi-compact
Quasi-separated
Tensor functor
Tannaka reconstruction

Cited by (0)