Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
created a section Contractible objects at lined topos.
This introduces and discusses a bit a notion of objects being contractible with respect to a specified line object (maybe the section deserves to be at interval object instead, not sure).
This notion is something I made up, so review critically. I am open for suggestions of different terminology. The concept itself, simple as it is (though not entirely trivial), I need for the discussion of path oo-groupoids of oo-stacks on my personal web:
if a lined Grothendieck topos is such that all representable objects are contractible with respect to the line object , then the path oo-groupoid functor
on simplicial sheaves, which a priori is only a Qulillen functor of oo-prestacks, enhances to a Quillen functor of oo-stacks (i.e. respects the local weak equivalences).
<div>
<blockquote>
if a lined Grothendieck topos is such that all representable objects are contractible with respect to the line object R, then the path oo-groupoid functor
on simplicial sheaves, which a priori is only a Qulillen functor of oo-prestacks, enhances to a Quillen functor of oo-stacks
</blockquote>
<p>The proof for that, by the way, is now typed up in the section <a href="http://ncatlab.org/schreiber/show/path+%E2%88%9E-groupoid#the_local_quillen_adjunction_13">Local Quillen adjunction</a> at <a href="http://ncatlab.org/schreiber/show/path+%E2%88%9E-groupoid">path oo-groupoid</a> on my personal web.</p>
</div>
added one more example at lined topos in the section Contractible objects: on contractible objects in smooth toposes
1 to 3 of 3