Mathematical Research Letters

Volume 26 (2019)

Number 4

Universal factorization spaces and algebras

Pages: 1059 – 1096



Emily Cliff (Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Il., U.S.A.)


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.

Received 20 March 2017

Accepted 11 March 2019

Published 25 October 2019