Condensed Learning Seminar

Dualizable Categories

Introduce the notion of stable compactly generated -category and discuss its properties and some examples. In particular, prove that the -category of small idempotent complete stable -categories is equivalent to the -category of compactly generated stable -categories with strongly continuous functors. After that, recall the definition of dualizable object in a symmetric monoidal ()category. Briefly review the Lurie tensor product of (stable) presentable -categories and then discuss the notion of dualizable stable -categories. Prove some of its equivalent characterizations: as retracts of compactly generated stable -categories, in terms of the double left adjoint to the Yoneda embedding, and in terms of compact maps. If time permits, prove that the -category of sheaves of spectra on a locally compact Hausdorff topological space is dualizable. 

Date & Time

February 09, 2024 | 2:30pm – 4:30pm

Location

Princeton University, Fine Hall 314

Event Series