The affine Hecke category is a monoidal colimit

Abstract

Let $G$ be a semisimple simply-connected algebraic group over an algebraically closed field of characteristic zero. We prove that the affine Hecke category associated to the loop group of $G$ is equivalent to the colimit, evaluated in the $\infty$-category of monoidal stable $\infty$-categories, of the finite type Hecke subcategories associated to standard parahoric subgroups. The main ingredient is an inductive characterization of colimits indexed by (sufficiently nice) bistratified categories. Our method is very general and can be used to prove a number of analogous 'colimit theorems,' e.g. for D-modules on the loop group.

45 pages. The main theorem is now proved in a simpler way; see Section 1.5. Readers looking for the 'convolution Schubert 1-category' should consult v3

References in corpus (5)

• Higher Topos Theory
• Loop group actions on categories and Whittaker invariants
• Reedy categories and their generalizations
• Homotopical presentations of braid groups via reduced lifts
• A colimit presentation of $\mathcal{D}(G(K))$ via the Bott-Samelson hypercover

Cited by in corpus (2)

• A colimit presentation of $\mathcal{D}(G(K))$ via the Bott-Samelson hypercover
• Homotopical presentations of braid groups via reduced lifts