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SUMMARY:Keisuke Hoshino (Kyoto University)
DTSTART:20241029T235900Z
DTEND:20241030T010000Z
DTSTAMP:20260409T130258Z
UID:SecondVDCW/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SecondVDCW/6
 /">Double categories of relations relative to factorisation systems</a>\nb
 y Keisuke Hoshino (Kyoto University) as part of Second Virtual Workshop on
  Double Categories\n\n\nAbstract\nThe double category of relations and the
  double category of spans have historically been key examples in the study
  of double categories. More generally\, given a class $\\mathcal{M}$ of mo
 rphisms in a finitely complete category $\\mathbf{C}$\, one can define an 
 $\\mathcal{M}$-relation $A \\nrightarrow B$ as a span that belongs to $\\m
 athcal{M}$ as a morphism into $A\\times B$. If $\\mathcal{M}$ is the right
  class of a stable factorisation system\, the $\\mathcal{M}$-relations and
  morphisms in $\\mathbf{C}$ form a double category.\n\nIn this talk\, I wi
 ll first give a characterisation of double categories that arise from stab
 le factorisation systems in this manner.\n\nI will then explore how differ
 ent classes of stable factorisation systems can be characterised in terms 
 of their corresponding double categories. This include the (regular epi\, 
 mono) factorisation system on a regular category\, which has been studied 
 by Carboni and Walters in terms of cartesian bicategories\, and by Lambert
  in terms of cartesian double categories. By considering the (isomorphism\
 , all) factorisation system\, we also recover the double category of spans
 \, a structure that has been examined bicategorically by Lack\, Walters\, 
 and Wood\, and double-categorically by Aleiferi. I will explain how these 
 known results are related to our general theorem.\n\nThis talk is based on
  joint work with Hayato Nasu\, and the results can be found in our paper a
 vailable at https://arxiv.org/abs/2310.19428.\n
LOCATION:https://researchseminars.org/talk/SecondVDCW/6/
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