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
With braiding
With duals for objects
category with duals (list of them)
dualizable object (what they have)
ribbon category, a.k.a. tortile category
With duals for morphisms
monoidal dagger-category?
With traces
Closed structure
Special sorts of products
Semisimplicity
Morphisms
Internal monoids
Examples
Theorems
In higher category theory
The yoga of handling tensors, in particular contracting them with each other; and in the case of tensor products of sections of a tangent bundle and cotangent bundle also the operations of differentiation of tensors, hence the generalization of “calculus” (analysis) from vectors to tensors.
See at string diagram and tensor network for more.
Last revised on February 3, 2019 at 10:46:24. See the history of this page for a list of all contributions to it.