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CATEGORIES:Category Theory Seminar
SUMMARY:Isotropy Groups of Quasi-Equational Theories - Jas
on Parker\, Brandon University
DTSTART;TZID=Europe/London:20201201T141500
DTEND;TZID=Europe/London:20201201T151500
UID:TALK154522AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/154522
DESCRIPTION:In [2]\, my PhD supervisors (Pieter Hofstra and Ph
ilip Scott)\nand I studied the new topos-theoretic
phenomenon of isotropy (as\nintroduced in [1]) in
the context of single-sorted algebraic theories\,
\nand we gave a logical/syntactic characterization
of the\nisotropy group of any such theory\, there
by showing that it encodes a\nnotion of inner auto
morphism or conjugation for the theory. In the\npr
esent talk\, I will summarize the results of my re
cent\nPhD thesis\, in which I build on this earlie
r work by studying the\nisotropy groups of (multi-
sorted) quasi-equational theories (also\nknown as
essentially algebraic\, cartesian\, or finite limi
t theories).\nIn particular\, I will show how\nto
give a logical/syntactic characterization of the i
sotropy group of\nany such theory\, and that it en
codes a notion of inner automorphism or\nconjugati
on for the theory. I will also describe how I have
used this\ncharacterization to exactly\ncharacter
ize the ‘inner automorphisms’ for several differen
t examples\nof quasi-equational theories\, most no
tably the theory of strict\nmonoidal categories an
d the theory of presheaves valued in a category\no
f models. In particular\, the latter example provi
des a\ncharacterization of the (covariant) isotrop
y group of a category of\nset-valued presheaves\,
which had been an open question in the theory\nof
categorical isotropy.\n[1] J. Funk\, P. Hofstra\,
B. Steinberg. Isotropy and crossed toposes.\nTheor
y and Applications of Categories 26\, 660-709\, 20
12.\n[2] P. Hofstra\, J. Parker\, P.J. Scott. Isot
ropy of algebraic theories.\nElectronic Notes in T
heoretical Computer Science 341\, 201-217\, 2018.\
n\nZoom link: https://maths-cam-ac-uk.zoom.us/j/9
1679283736?pwd=Sm04c1ZqaFcxVzBLT2Z3cnpNZVpKUT09\n\
nMeeting ID: 916 7928 3736\nPasscode: 844306\n
LOCATION:Zoom (Meeting ID 916 7928 3736\, passcode 844306)
CONTACT:José Siqueira
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