Universal factorization spaces and algebras

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 étale 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.

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

References in corpus (2)

• Higher Topos Theory
• Formal loops IV: Chiral differential operators

Cited by in corpus (4)

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