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SUMMARY:Well-pointed endofunctor on (\\infty\,1)-category (UCLouvain-ULB-V
 UB Category Theory Seminar )
DTSTART:20250708T141500Z
DTEND:20250708T151500Z
DTSTAMP:20260916T062800Z
UID:indico-event-5564@agenda.irmp.ucl.ac.be
DESCRIPTION:Speakers: Simon Henry (UOttawa)\n\n Well-pointed endofunctors
  are a tool developed by Kelly in the 80s to formalize most of the “tran
 sfinite iterative construction” we encounter in category theory. That is
 \, construction of new objects in a category by repeating a given process 
 an infinite number of times\, until it hopefully converges. This includes\
 , for example\, colimits in the category of algebras for a monad\, free al
 gebras over endofunctors and pointed endofunctors\, free monoids\, formall
 y inverting an element in a commutative monoid\, etc...In this talk I will
  present how this theory generalizes to the setting of (∞\, 1)-categorie
 s\, though most of the interesting phenomena are happening at the level of
  2-categories\, so no knowledge of ∞-category theory is strictly require
 d.Most of the time\, generalizing a result from 1-category theory to (∞\
 , 1)-category theory is relatively straightforward: Once the 1-category th
 eoretic result is presented in a sufficiently nice way\, we can just trans
 late it to the ∞-categorical context\, to obtain a formally very similar
  result\, by just replacing the basic category theory results used in the 
 proof with their higher categorical analogues. In the rare case where one 
 of the basic results hasn’t been established for higher categories yet\,
  we need to establish it\, generally using a model-dependent argument. Thi
 s talk is about a case where things did not work like this at all: the the
 ory of well-pointed endofunctors on higher categories turn out to look qui
 te different from its 1-categorical counterpart: In the higher categorical
  setting of the theory\, there is an additional obstruction to the converg
 ence of the iteration that appears at the level of 2-cells\, and is relate
 d to braid groups.\n\nhttps://agenda.irmp.ucl.ac.be/event/5564/
LOCATION:B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cy
 clotron\, 2\, Louvain-la-Neuve))
URL:https://agenda.irmp.ucl.ac.be/event/5564/
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