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SUMMARY:Isotropy Groups of Quasi-Equational Theories - Jason Parker\, Bran
 don University
DTSTART:20201201T141500Z
DTEND:20201201T151500Z
UID:TALK154522@talks.cam.ac.uk
CONTACT:José Siqueira
DESCRIPTION:In [2]\, my PhD supervisors (Pieter Hofstra and Philip Scott)\
 nand I studied the new topos-theoretic phenomenon of isotropy (as\nintrodu
 ced in [1]) in the context of single-sorted algebraic theories\,\nand we g
 ave a logical/syntactic characterization of the\nisotropy group of any suc
 h theory\, thereby showing that it encodes a\nnotion of inner automorphism
  or conjugation for the theory. In the\npresent talk\, I will summarize th
 e results of my recent\nPhD thesis\, in which I build on this earlier work
  by studying the\nisotropy groups of (multi-sorted) quasi-equational theor
 ies (also\nknown as essentially algebraic\, cartesian\, or finite limit th
 eories).\nIn particular\, I will show how\nto give a logical/syntactic cha
 racterization of the isotropy group of\nany such theory\, and that it enco
 des a notion of inner automorphism or\nconjugation for the theory. I will 
 also describe how I have used this\ncharacterization to exactly\ncharacter
 ize the ‘inner automorphisms’ for several different examples\nof quasi
 -equational theories\, most notably the theory of strict\nmonoidal categor
 ies and the theory of presheaves valued in a category\nof models. In parti
 cular\, the latter example provides a\ncharacterization of the (covariant)
  isotropy group of a category of\nset-valued presheaves\, which had been a
 n open question in the theory\nof categorical isotropy.\n[1] J. Funk\, P. 
 Hofstra\, B. Steinberg. Isotropy and crossed toposes.\nTheory and Applicat
 ions of Categories 26\, 660-709\, 2012.\n[2] P. Hofstra\, J. Parker\, P.J.
  Scott. Isotropy of algebraic theories.\nElectronic Notes in Theoretical C
 omputer Science 341\, 201-217\, 2018.\n\nZoom link:  https://maths-cam-ac-
 uk.zoom.us/j/91679283736?pwd=Sm04c1ZqaFcxVzBLT2Z3cnpNZVpKUT09\n\nMeeting I
 D: 916 7928 3736\nPasscode: 844306\n
LOCATION:Zoom (Meeting ID 916 7928 3736\, passcode 844306)
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