Universal factorization spaces and algebras
Algebraic Geometry
2019-11-06 v2
Abstract
We introduce categories of weak factorization algebras and factorization spaces, and prove that they are equivalent to the categories of ordinary factorization algebras and spaces, respectively. This allows us to define the pullback of a factorization algebra or space by an \'etale morphism of schemes, and hence to define the notion of a universal factorization space or algebra. This provides a generalization to higher dimensions and to non-linear settings of the notion of a vertex algebra.
Cite
@article{arxiv.1608.08122,
title = {Universal factorization spaces and algebras},
author = {Emily Cliff},
journal= {arXiv preprint arXiv:1608.08122},
year = {2019}
}
Comments
28 pages. In version 2, more details have been added to proofs relating to factorization algebras (as compared to factorization spaces). The paper has been reorganized to accommodate this additional material