nLab
2Mod

Contents

Contents

Idea

The 2-category of 2-modules/2-vector spaces.

Fix some commutative ring or more generally an E-infinity ring RR. Then a basis for a 2-module/2-vector space over RR may be taken to be an RR-associative algebra or more generally an RRMod-enriched category 𝒜\mathcal{A} (an algebras): the correspponding 2-vector space is the category of modules Hom RMod(𝒜,RMod)Hom_{R Mod}(\mathcal{A}, R Mod). Then 2Mod R2Mod_R is equivalently the 2-category whose

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

2Mod R=Mod(Mod R) 2Mod_R = Mod(Mod_R)

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

Algebra objects in 2Mod2Mod

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

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.