nLab
tensor calculus

Contents

Context

Linear algebra

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

Monoidal categories

monoidal categories

With symmetry

With duals for objects

With duals for morphisms

With traces

Closed structure

Special sorts of products

Semisimplicity

Morphisms

Internal monoids

Examples

Theorems

In higher category theory

Contents

Idea

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.

Wikipedia

Last revised on February 3, 2019 at 05:46:24. See the history of this page for a list of all contributions to it.