Lectures on Higher Categories
March 2025
Plan
- Part 1: (∞,1)-categories: models and practice, universal constructions, (un)straightening equivalence, cofinality, Yoneda and presheaves, Presentable categories and localizations, stable categories, spectra, associative and commutative algebras, animation, monadicity.
- Special talk on enriched ∞-categories by Markus Zetto.
- Part 2: the (∞,1)-category of (∞,n)-categories. Strict methods and the Steiner theory. Lax transformations and Gray tensor product. Categorical Spectra and stability. Adjunction, TQFTs and factorization homology.
Notes
day 1 notes and exercises
day 2 exercises
lecture 4
presentable stuff
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