nLab model structure on modules in a monoidal model category

Contents

Context

Model category theory

model category, model \infty -category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

Presentation of (,1)(\infty,1)-categories

Model structures

for \infty-groupoids

for ∞-groupoids

for equivariant \infty-groupoids

for rational \infty-groupoids

for rational equivariant \infty-groupoids

for nn-groupoids

for \infty-groups

for \infty-algebras

general

specific

for stable/spectrum objects

for (,1)(\infty,1)-categories

for stable (,1)(\infty,1)-categories

for (,1)(\infty,1)-operads

for (n,r)(n,r)-categories

for (,1)(\infty,1)-sheaves / \infty-stacks

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

Higher algebra

Contents

Idea

For 𝒞\mathcal{C} a monoidal model category and AMon(𝒞)A \in Mon(\mathcal{C}) a monoid in 𝒞\mathcal{C}, there is under mild conditions a natural model category structure on its category of modules over AA. (Schwede & Shipley 2000, Thm. 4.1 (3.1 in the preprint)).

References

General discussion:

The special case of the model structure on modules in a functor category with values in a closed symmetric monoidal model category is (re-)derived (see the discussion here) in:

(there for the purpose of desribing representations of nets of observables in homotopical algebraic quantum field theory).

Last revised on May 31, 2022 at 04:55:46. See the history of this page for a list of all contributions to it.