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model structure on algebras over a monad

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Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

Presentation of (∞,1)-categories

Model structures

for ∞-groupoids

for ∞-groupoids

for n-groupoids

for ∞-groups

for ∞-algebras

general

specific

for stable/spectrum objects

for (∞,1)-categories

for stable (∞,1)-categories

for (∞,1)-operads

for (n,r)-categories

for (∞,1)-sheaves / ∞-stacks

Higher algebra

higher algebra

universal algebra

Algebraic theories

Algebras and modules

Higher algebras

Model category presentations

Geometry on formal duals of algebras

Theorems

Contents

Idea

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

Definition

Let C be a cofibrantly generated model category and T:C→C a monad on C.

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

(F⊣U):AlgT→U←FC.(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)
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