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SUMMARY:Pre-sheaves of spaces and the Grothendieck construction in higher 
 geometry - Danny Stevenson (University of Adelaide)
DTSTART:20170331T123000Z
DTEND:20170331T133000Z
UID:TALK71716@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The notion of pre-stack in algebraic geometry can be formulate
 d either in terms of categories fibered in groupoids\, or else as a functo
 r to the category of groupoids with composites only preserved up to a cohe
 rent system of natural isomorphisms. &nbsp\;The device which lets one shif
 t from one perspective to the other is known as the `Grothendieck construc
 tion&#39\; in category theory. &nbsp\;<br>A pre-sheaf in higher geometry i
 s a functor to the &infin\;-category of &infin\;-groupoids\; in this conte
 xt keeping track of all the coherent natural isomorphisms between composit
 es becomes particularly acute. &nbsp\;Fortunately there is an analog of th
 e Grothendieck construction in this context\, due to Lurie\, which lets on
 e `straighten out&#39\; a pre-sheaf into a certain kind of fibration. &nbs
 p\;In this talk we will give a new perspective on this straightening proce
 dure which allows for a more conceptual proof of Lurie&#39\;s straightenin
 g theorem.&nbsp\;<br><br>
LOCATION:Seminar Room 1\, Newton Institute
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