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SUMMARY:Nima Rasekh (Universität Greifswald)
DTSTART:20241024T080000Z
DTEND:20241024T090000Z
DTSTAMP:20260409T132430Z
UID:SecondVDCW/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SecondVDCW/3
 /">Double Categories in Univalent Foundations</a>\nby Nima Rasekh (Univers
 ität Greifswald) as part of Second Virtual Workshop on Double Categories\
 n\n\nAbstract\nThis is joint work with Niels van der Weide\, Benedikt Ahre
 ns and Paige Randall North. In category theory\, we typically study catego
 ries either up to isomorphisms (considering objects up to equality) or equ
 ivalences (considering objects up to isomorphism). Fortunately\, since equ
 ivalences generalize isomorphisms\, this distinction rarely causes mathema
 tical difficulties. However\, double categories present a richer structure
  with multiple notions of equivalence—such as isomorphisms\, horizontal 
 equivalences\, and gregarious equivalences—none of which subsumes all th
 e others. This creates potential ambiguities\, making it necessary to spec
 ify the appropriate form of equivalence in any given context. In this talk
 \, I will show how moving from a set-theoretic foundation to a univalent f
 oundation allows for definitions of (double) categories that inherently in
 clude the desired notion of equivalence.\n
LOCATION:https://researchseminars.org/talk/SecondVDCW/3/
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