**natural deduction** metalanguage, practical foundations

**type theory** (dependent, intensional, observational type theory, homotopy type theory)

**computational trinitarianism** =

**propositions as types** +**programs as proofs** +**relation type theory/category theory**

**homotopy theory, (∞,1)-category theory, homotopy type theory**

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…

models: topological, simplicial, localic, …

see also **algebraic topology**

**Introductions**

**Definitions**

**Paths and cylinders**

**Homotopy groups**

**Basic facts**

**Theorems**

On “natural” models (Awodey 2016) of homotopy type theory. For the moment see there.

- Steve Awodey,
*Natural models of homotopy type theory*, Mathematical Structures in Computer Science,**28**2 (2016) 241-286 $[$arXiv:1406.3219, doi:10.1017/S0960129516000268$]$

Last revised on June 7, 2022 at 02:41:59. See the history of this page for a list of all contributions to it.