Tensor functors between categories of quasi-coherent sheaves
Algebraic Geometry
2014-10-07 v2 Category Theory
Abstract
For a quasi-compact quasi-separated scheme X and an arbitrary scheme Y we show that the pullback construction implements an equivalence between the discrete category of morphisms Y --> X 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 Durov's notion of generalized schemes over F_1.
Keywords
Cite
@article{arxiv.1202.5147,
title = {Tensor functors between categories of quasi-coherent sheaves},
author = {Martin Brandenburg and Alexandru Chirvasitu},
journal= {arXiv preprint arXiv:1202.5147},
year = {2014}
}
Comments
22 pages; revised version