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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Pre-sheaves of spaces and the Grothendieck constru
ction in higher geometry - Danny Stevenson (Univer
sity of Adelaide)
DTSTART;TZID=Europe/London:20170331T133000
DTEND;TZID=Europe/London:20170331T143000
UID:TALK71716AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/71716
DESCRIPTION:The notion of pre-stack in algebraic geometry can
be formulated either in terms of categories fibere
d in groupoids\, or else as a functor to the categ
ory of groupoids with composites only preserved up
to a coherent system of natural isomorphisms. &nb
sp\;The device which lets one shift from one persp
ective to the other is known as the `Grothendieck
construction'\; in category theory. \;

A pre-sheaf in higher geometry is a functor to the
&infin\;-category of &infin\;-groupoids\; in this
context keeping track of all the coherent natural
isomorphisms between composites becomes particula
rly acute. \;Fortunately there is an analog o
f the Grothendieck construction in this context\,
due to Lurie\, which lets one `straighten out'\
; a pre-sheaf into a certain kind of fibration. &n
bsp\;In this talk we will give a new perspective o
n this straightening procedure which allows for a
more conceptual proof of Lurie'\;s straightenin
g theorem. \;

LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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