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SUMMARY:Aaron David Fairbanks (Dalhousie University)
DTSTART:20261106T164500Z
DTEND:20261106T173000Z
DTSTAMP:20261030T095013Z
UID:ThirdVWDC/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ThirdVWDC/6/
 ">Doubly weak double categories</a>\nby Aaron David Fairbanks (Dalhousie U
 niversity) as part of Third Virtual Workshop on Double Categories\n\n\nAbs
 tract\nDouble categories are typically weak in one direction: the horizont
 al (or "loose") 1-cells compose weakly associatively as in a bicategory (a
 .k.a. weak 2-category)\, whereas the vertical (or "tight") 1-cells compose
  strictly associatively as in a strict 2-category. There have been various
  attempts to define double categories with weakly associative composition 
 in both directions. This is desirable in order to capture a broader range 
 of examples\, as well as to obtain a more symmetric theory. What is puzzli
 ng is that trying to straightforwardly generalize the usual definition lea
 ds into deadlock around coherence conditions.\n\nWe introduce a surprising
 ly easy definition that involves no coherence conditions. It arises as the
  double-categorical analogue of a surprisingly easy definition of bicatego
 ry that involves no coherence conditions. We then connect this definition 
 to other definitions that are more analogous to the usual definition of bi
 category. In particular we show our doubly weak double categories are equi
 valent to Verity's double bicategories satisfying a mild condition that al
 ready appears in the literature\, and they are equivalent to Garner's cubi
 cal bicategories satisfying a similar condition. Joint work with Michael S
 hulman.\n
LOCATION:https://researchseminars.org/talk/ThirdVWDC/6/
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