*categories: Seminar talk by Paul Taylor on Thursday March 2 2022@ 2023-02-28 12:23 Niccolò Veltri0 siblings, 0 replies; only message in thread From: Niccolò Veltri @ 2023-02-28 12:23 UTC (permalink / raw) To: categories Hi everyone, On Thursday March 2 2023 at 4pm EET (2pm UTC), Paul Taylor will give a presentation on well founded coalgebras. This is a shared event in the seminar series of the "Logic and Semantics" group at Tallinn University of Technology and the "Theory Group" of the School of Computer Science at the University of Birmingham. Everyone is invited to participate! Details on how to access the talk on Zoom are available on any of the following webpages: https://www.paultaylor.eu/ordinals/ http://talks.bham.ac.uk/talk/index/5159 https://niccoloveltri.github.io/tsem22/taylor0203.html Title and abstract of the talk are below. Best, Niccol?? --- "Well Founded Coalgebras" Paul Taylor Categorical set theory explores ideas taken from set theory to develop mathematics using category theoretic tools. It began in the 1970s when Mikkelsen and Osius interpreted recursion and epsilon-structures in an elementary topos. Well founded coalgebras generalise epsilon-structures to give approximations to the free algebra for a functor even when this does not exist. The main recursion theorem is based on the one of von Neumann for ordinals. Originally that was based on fixed points in complete lattices, but in order to consider more general categories and functors, we must use Pataraia's Theorem for dcpos instead. However, for our more complicated constructions, we need to find a scalpel not a sledgehammer, so a more subtle form of Pataraia's Theorem is developed. The paper develops analogues of the recursion theorem and Mostowski extensional quotient potentially in much more general categories, with factorisation systems intead of 1-1 functions. The obvious first application of this generalisation replaces Set with Pos to study the different forms of intuitionistic ordinals that were introduced in the 1990s. This in turn leads to a formulation of transfinite iteration of functors, based on a categorical axiom instead of the set-theoretic axiom-scheme of replacement. See?? www.paultaylor.eu/ordinals/?? for full details. [For admin and other information see: http://www.mta.ca/~cat-dist/ ] ^ permalink raw reply [flat|nested] only message in thread

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