# nLab linear magmoid

Contents

### Context

#### Enriched category theory

enriched category theory

## Extra stuff, structure, property

### Homotopical enrichment

#### Algebra

higher algebra

universal algebra

categorification

# Contents

## Idea

A linear magmoid is a magmoids whose hom-sets are all vector spaces (or modules) and whose composition operation is bilinear. This concept is an oidification of the concept of nonassociative nonunital algebra.

## Definitions

Fix a commutative ring $K$. (Often we want $K$ to be a field, such as the field $\mathbb{C}$ of complex numbers.)

A $K$-linear magmoid is a magmoid enriched over $K\,$Mod, the monoidal category of $K$-modules with the usual tensor product. (Note that we usually speak of $K\,$Vect instead of $K\,Mod$ when $K$ is a field.)

## Examples

Last revised on May 23, 2021 at 12:21:16. See the history of this page for a list of all contributions to it.