Little Cubes
Little Cube Algebras and Factorisation Homology
We are following Harpaz's notes, available here.
- Andres: 1–16
- Introduction
- Two models for $(\infty,1)$-categories
- Constructions of $\infty$-categories
- Severin: 16–30
- Left and right fibrations
- Cartesian and cocartesian fibrations
- Charles: 30–39
- The relative nerve
- Limits and colimits in $\infty$-categories
- Kan extensions
- William: 39–50
- Introduction [to symmetric monoidal $\infty$-categories]
- Examples and constructions
- Cartesian and cocartesian symmetric monoidal structures
- —: 50–58
- From colored operads to $\infty$-operads
- —: 58–69
- Weak $\infty$-operads and approximations
- Tensor products of $\infty$-operads
- —: 69–79
- Definitions and basic properties [of the little cube $\infty$-operads]
- Dunn's additivity theorem
- —: 79–88
- May's recognition principle
- —: 88–103
- Manifolds and framings
- Little cube algebras with tangent structures
- —: 103–115
- Little cube algebras over manifolds
- Factorization homology
- Axiomatic characterisation of factorization homology