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SUMMARY:Miloslav Štěpán (Masaryk University)
DTSTART:20241021T150000Z
DTEND:20241021T160000Z
DTSTAMP:20260409T134057Z
UID:SecondVDCW/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SecondVDCW/1
 /">Double categories versus factorization systems</a>\nby Miloslav Štěp
 án (Masaryk University) as part of Second Virtual Workshop on Double Cate
 gories\n\n\nAbstract\nIn the first part of the talk we will recall double 
 categories and show that\nevery orthogonal factorization system can be tur
 ned into a double category\,\nevery (nice) double category can be turned i
 nto an orthogonal factorization\nsystem\, and that these processes are mut
 ually inverse. We will do the same\nthing for strict factorization systems
 .\n\nIn the second part of the talk we will put the above results into a w
 ider\nperspective of 2-category theory: if the double category is regarded
  as a\ndiagram in Cat\, producing the factorization system out of it amoun
 ts to taking\na certain 2-categorial colimit of it (the codescent object).
  We will mention\nthe connections to lax morphisms of algebras for a 2-mon
 ad\, compositions of\npinwheels\, and possible extensions of the first par
 t to weak factorization\nsystems.\n
LOCATION:https://researchseminars.org/talk/SecondVDCW/1/
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