tensor

Contents

tensor#

The category of matrices with the Kronecker product as monoidal product.

Summary#

Dim

A dimension is a tuple of positive integers with product @ and unit Dim(1).

Tensor

A tensor is a Matrix with dimensions as domain and codomain and the Kronecker product as tensor.

Functor

A tensor functor is a frobenius functor with a domain category dom and Category(Dim, Tensor[dtype]) as codomain for a given dtype.

Diagram

A tensor diagram is a frobenius diagram with tensor boxes.

Box

A tensor box is a frobenius box with an array as data.

Swap

A tensor swap is a frobenius swap in a tensor diagram.

Cup

A tensor cup is a frobenius cup in a tensor diagram.

Cap

A tensor cap is a frobenius cap in a tensor diagram.

Spider

A tensor spider is a frobenius spider in a tensor diagram.

Sum

A formal sum of tensor diagrams with the same domain and codomain.

Bubble

Bubble in a tensor diagram, applies a function elementwise.