# nLab 2Mod

Contents

### Context

#### Higher algebra

higher algebra

universal algebra

# Contents

## Idea

Fix some commutative ring or more generally an E-infinity ring $R$. Then a basis for a 2-module/2-vector space over $R$ may be taken to be an $R$-associative algebra or more generally an $R$Mod-enriched category $\mathcal{A}$ (an algebras): the correspponding 2-vector space is the category of modules $Hom_{R Mod}(\mathcal{A}, R Mod)$. Then $2Mod_R$ is equivalently the 2-category whose

• objects are $R$-algebras;

In enriched category theory this is equivalently the 2-category of Mod${}_R$-enriched categories and profunctors between them. In this context one can write

$2Mod_R = Mod(Mod_R)$

or $2 Mod_R =$ Prof$(Mod_R)$ for this 2-category.

### Algebra objects in $2Mod$

An algebra object in 2Mod${}_3$ is equivalently a sesquiunital sesquialgebra over $R$. This may be taken to be a basis for a 3-module/3-vector space over $R$.

### Line 2-bundles

(…) line 2-bundle (…)

Last revised on July 19, 2013 at 10:13:02. See the history of this page for a list of all contributions to it.