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SUMMARY:Introduction to Cubical Higher Operads
DTSTART;VALUE=DATE-TIME:20171218T133000Z
DTEND;VALUE=DATE-TIME:20171218T143000Z
DTSTAMP;VALUE=DATE-TIME:20191116T232408Z
UID:indico-event-3091@indico.math.cnrs.fr
DESCRIPTION:In this talk we will start by explaining a spectacular analogy
between topological spaces and higher category theory : In [1] Michael Ba
tanin built the globular weak higher groupoid fundamental for any topologi
cal space X\, wished by Alexander Grothendieck. To do such construction he
used the coendomorphism operad associated to the coglobular object of dis
ks in Top\, the category of topological spaces. He was able to built the w
eak higher groupoid fundamental functor thanks to the contractibility of t
his operad. In the other hand the author [2] built a coglobular object in
the category of higher operads\, such that algebras for the first object a
re weak infini-categories\, algebras for the second object are weak infini
-functors\, etc. With such coglobular object we also get a coendomorphism
operad\, built itself with operads instead of topological spaces. We conje
cture that this operad is contractible like the topological one. If this i
s true then the globular weak higher category of globular weak higher cate
gories exist. Also we will explain how to build the free cubical contracti
ble higher operad which algebras are cubical weak higher categories\, and
if we have time we will explain how from this we obtain the cubical weak h
igher groupoid fundamental functor for topological spaces.\n\n\n[1] Michae
l Batanin\, Monoidal globular categories as a natural environment for the
theory of weak-n-categories\, Advances in Mathematics\, 1998.\n\n \n\n[2]
Camell Kachour\, Steps toward the weak higher category of weak higher cat
egories in the globular setting\, Category and Algebraic Structures with A
pplications\, 2015.\n\nhttps://indico.math.cnrs.fr/event/3091/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/3091/
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