nLab model structure on algebras over a monad

model category

Model structures

for ∞-groupoids

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

Higher algebra

higher algebra

universal algebra

Contents

Idea

For $\mathcal{C}$ a cofibrantly generated model category and $T \colon \mathcal{C} \longrightarrow \mathcal{C}$ a monad on $\mathcal{C}$, there is under mild conditions a natural model category structure on the category of algebras over a monad over $T$.

Definition

Let $\mathcal{C}$ be a cofibrantly generated model category and $T \colon \mathcal{C} \longrightarrow \mathcal{C}$ a monad on $\mathcal{C}$.

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

$(F \dashv U) \;\colon\; Alg_T(\mathcal{C}) \stackrel{\overset{F}{\longleftarrow}}{\underset{U}{\longrightarrow}} \mathcal{C} \,.$

References

Revised on October 5, 2016 14:34:31 by Urs Schreiber (89.204.153.227)