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 Discrete homotopy theory (also known as A-homotopy theory) is an area of mathematics concerned with using techniques of homotopy theory to study combinatorial properties of graphs. It does so by...