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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeDec 15th 2009
• (edited Dec 15th 2009)

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 $(\mathcal{T} = Sh(C),R)$ is such that all representable objects are contractible with respect to the line object $R$, then the path oo-groupoid functor

$\Pi : SSh(C) \to SSh(C)$

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).

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeDec 15th 2009
This comment is invalid XHTML+MathML+SVG; displaying source. <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>
• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeDec 22nd 2009

added one more example at lined topos in the section Contractible objects: on contractible objects in smooth toposes