nLab
model structure on algebras over a monad
Contents
Context
Model category theory
model category, model -category
Definitions
Morphisms
Universal constructions
Refinements
Producing new model structures
Presentation of -categories
Model structures
for -groupoids
for ∞-groupoids
for equivariant -groupoids
for rational -groupoids
for rational equivariant -groupoids
for -groupoids
for -groups
for -algebras
general
specific
for stable/spectrum objects
for -categories
for stable -categories
for -operads
for -categories
for -sheaves / -stacks
Higher algebra
Contents
Idea
For a cofibrantly generated model category and a monad on , there is under mild conditions a natural model category structure on the category of algebras over a monad over .
Definition
Let be a cofibrantly generated model category and a monad on .
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
See (Schwede-Shipley 00, lemma 2.3).
References
Last revised on October 5, 2016 at 14:34:31.
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