4.2 Article

Derived loop stacks and categorification of orbifold products

Journal

JOURNAL OF NONCOMMUTATIVE GEOMETRY
Volume 13, Issue 3, Pages 963-983

Publisher

EUROPEAN MATHEMATICAL SOC
DOI: 10.4171/JNCG/342

Keywords

Orbifold products; categorification; loop space

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The existence of interesting multiplicative cohomology theories for orbifolds was initially suggested by string theorists. Orbifold products have been intensely studied by mathematicians for the last fifteen years. In this paper we focus on the virtual orbifold product that was first introduced in Lupercio et al. (2007). We construct a categorification of the virtual orbifold product that leverages the geometry of derived loop stacks. After work of Ben-Zvi Francis and Nadler, this reveals connections between virtual orbifold products and Drinfeld centers of monoidal categories, thus answering a question of Hinich.

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