#
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 $(\infty,1)$-categories

## Model structures

### for $\infty$-groupoids

for ∞-groupoids

### for $n$-groupoids

### for $\infty$-groups

### for $\infty$-algebras

#### general

#### specific

### for stable/spectrum objects

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

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

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

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

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

#### Higher algebra

# Contents

## Idea

For $C$ a monoidal model category and $T : C \to C$ 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 $T : C \to C$ 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

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

See (SchwedeShipley, lemma 2.3).

## References

Revised on November 18, 2010 15:56:02
by

Urs Schreiber
(131.211.232.149)