Infinity category seminar

• Coordinates
• Fall 2022: sets and categories
• Winter 2023: groups, rings, and modules
• References

Coordinates#

• Location: 380-384I
• Time: Thursdays at 3:00–4:20pm

Fall 2022: sets and categories#

• Introduction
• Simplicial sets
• ∞-categories
• Constructing ∞-categories
• Limits and colimits
• The ∞-category of sheaves
• Stable ∞-categories
• Nonabelian derived functors
• The cotangent complex

Winter 2023: groups, rings, and modules#

• Recollections and loose ends
• t-structures and Dold–Kan
• Examples of stable ∞-categories
• ∞-operads
• Algebras and modules
• Ring spectra
• Properties of modules
• Spectral schemes
• The cotangent complex revisited
• Examples of ∞-rings

References#

Kerodon is referenced by the tag number. For instance, the definition of Kan complexes is at https://kerodon.net/tag/002H, so we refer to the definition by Definition 002H.

1. Kerodon: Lurie, Kerodon.
2. HA: Lurie, Higher Algebra.
3. HTT: Lurie, Higher Topos Theory.
4. SAG: Lurie, Spectral Algebraic Geometry.