nLab
model structure on algebras over a monad

Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

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

Model structures

for \infty-groupoids

for ∞-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

Higher algebra

Contents

Idea

For CC a monoidal model category and T:CCT : C \to C a monad on CC, there is under mild conditions a natural model category structure on the category of algebras over a monad over TT.

Definition

Let CC be a cofibrantly generated model category and T:CCT : C \to C a monad on CC.

Then under mild conditions there exists the transferred model structure on the category of algebras over a monad, transferred along the free functor/forgetful functor adjunction

(FU):AlgTUFC. (F \dashv U) : Alg T \stackrel{\overset{F}{\leftarrow}}{\underset{U}{\to}} C \,.

See (SchwedeShipley, lemma 2.3).

References

Revised on November 18, 2010 15:56:02 by Urs Schreiber (131.211.232.149)