model structure on reduced simplicial sets
Model category theory
Producing new model structures
Presentation of -categories
for stable/spectrum objects
for stable -categories
for -sheaves / -stacks
The model structure on reduced simplicial sets is a presentation of the full sub-(∞,1)-category
∞Grpd ∞Grpd Top
of pointed ∞-groupoids on those that are connected.
By the looping and delooping-equivalence, this is equivalent to the (∞,1)-category of ∞-groups and this equivalence is presented by a Quillen equivalence to the model structure on simplicial groups.
This appears as (GoerssJardine, ch V, prop. 6.2).
This appears as (GoerssJardine, ch. V prop. 6.3).
Under the forgetful functor
- a fibration maps to a fibration precisely if it has the right lifting property against ;
- every fibrant object maps to a fibrant object.
The first statment appears as (GoerssJardine, ch. V, lemma 6.6.). The second (an immediate consequence) appears as (GoerssJardine, ch. V, corollary 6.8).
A standard textbook reference is chapter V of
Revised on March 10, 2016 04:36:07
by Urs Schreiber