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  • stable infinity category

Model category theory

Definitions

• Definition of a model category:

Topics

classical category theory - Serre fibration - Fibrant object - Cofibrant object - [Cofibrant generation](Cofibrant generati - Weak equivalence - localization (category theory) - the model structure on spectra

Applies to Chain Complexes

• derived functor
• homotopy category
• The model structure on chain complexes

Model Cat Specific

• Quillen equivalence
• Quillen adjunction -on)
• The model structure on simplicial sets

Notes

Let \({ \mathcal{N}({{-}}) }_{{\mathsf{dg}}}\) be the DG nerve functor, then

Being local:

• Important: the small object argument

See Quillen adjunction

Model structure on sSet

Model structure on Top

Model structure on spectra

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