A homotopy 2-category is a category made up of:
- 0-cells that are some notion of infinity-categories, or space.
- 1-cells that encode a notion of an infinity-functor or continuous map.
- 2-cell that encodes a notion of an infinity-Natural Transformation or Homotopy Theory between maps.
These are defined by a model and used in riehl2019-infinity-categories to axiomatically define Weak-Infinity Categories. The main axiom needed is that every possible way of composing 2-cells produces an equal composite 2-cell.