You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
Graham Manuell (Jul 29 2024 at 16:04):The category theory research group which I am a part of, at Stellenbosch University in South Africa, has recently started a hybrid research seminar in category theory (in collaboration with NITheCS). We have weekly sessions currently on Tuesdays at 12:10-13:00 UTC+02:00 which can be attended on Zoom. Anyone who is interested to attend or contribute a talk is welcome! Please send an email to @Roy Ferguson at rferguson@sun.ac.za to be placed on the mailing list or to request to give a talk.
Nathanael Arkor (Jul 29 2024 at 16:06):Is there a schedule online somewhere?
Graham Manuell (Jul 29 2024 at 16:10):I will be giving the talk tomorrow. It will be the first part of a series of talks that will run over the next few weeks (with break of two weeks in the middle).
Speaker: Graham Manuell
Title: Workshop on pointfree topology and constructive mathematics - part 1
Date and time: -
Zoom registration link: https://bit.ly/4fqjRmQ
Abstract:Constructive logic is a generalisation of classical logic that applies in more situations, including mathematical universes (toposes) where propositions can take different values at different locations in some space or where every function from to is computable. Unfortunately, in this general setting many classical results of point-set topology fail. However, almost all of these results can be recovered if we reformulate topology in terms of lattices of opens without predefined underlying sets of points. Moreover, this perspective also sheds light on many not-obviously-topological aspects of constructive mathematics itself.
In the first lecture of this series, I will motivate and introduce the notions of frames and locales and begin to discuss intuitionistic logic and basic concepts in constructive mathematics.
Graham Manuell (Jul 29 2024 at 16:12):Nathanael Arkor said:
Is there a schedule online somewhere?
The talks are usually only planned about one week in advance, but you can see scheduled talks on the NITheCS website. Announcements will also go out on our mailing list. We will probably also mention the talks here, at least in the near future.
David Egolf (Jul 29 2024 at 16:21):Will a recording be made available for tomorrow's talk? The talk sounds interesting, but it's at ~3 AM for me.
Roy Ferguson (Jul 29 2024 at 16:28):Yes! Recordings of sessions are on the NITheCS YouTube page https://www.youtube.com/@nithecs
Graham Manuell (Aug 05 2024 at 13:23):The video from last week is up on YouTube.
Graham Manuell (Aug 05 2024 at 13:24):Tomorrow is part two of the above series.
Speaker: Graham Manuell
Title: Workshop on pointfree topology and constructive mathematics - part 2
Date and time: -
Link: https://bit.ly/3SxYhmS
Abstract: This week we will continue to discuss intuitionistic logic and introduce presentations of frames.
Graham Manuell (Aug 12 2024 at 12:48):We will take a break from the above series for the next two weeks, but there will still be another talk tomorrow.
Graham Manuell (Aug 12 2024 at 12:52):Speaker: Zurab Janelidze
Title: Isbell's subfactor projections in a noetherian form
Date and time: -
Zoom registration link: TBA
Abstract:
In this talk we give an outline of a paper by the same title (joint work with Kishan Dayaram and Amartya Goswami), recently submitted for publication. In this paper, we revisit the 1979 work of Isbell on subfactors of groups and their projections, which he uses to establish a stronger formulation of the butterfly lemma and its consequence, the refinement theorem for subnormal series of subgroups. We point out an error in the second part of Isbell's refinement theorem but show that the rest of his results can be extended to the general self-dual context of a noetherian form, which includes in its scope all semi-abelian categories as well as all Grandis exact categories. Furthermore, we show that Isbell's formulations of the butterfly lemma and the refinement theorem amount to canonicity of isomorphisms established in these results.
Speaker Bio:
Zurab Janelidze is a Professor of Mathematics in the Department of Mathematical Sciences at Stellenbosch University. He is a Principal Investigator in the Mathematical Structures and Modelling research programme at NITheCS. He serves on the editorial boards of two international journals in his field of expertise, category theory, as well as Afrika Matematika (the journal of the African Mathematical Union), and currently serves as the president of the South African Mathematical Society.
Roy Ferguson (Aug 12 2024 at 14:02):Hello! The Zoom registration link for this talk is https://bit.ly/3X1s4XJ
Roy Ferguson (Aug 26 2024 at 14:11):Hello :wave: Graham will be resuming the workshop series on pointfree topology and constructive mathematics tomorrow. The details are as follows.
Speaker: Graham Manuell
Title: Workshop on pointfree topology and constructive mathematics - part 3
Date and time: Tue, 27 Aug 2024, 12:10 pm-Tue, 27 Aug 2024, 1:00 pm
Zoom registration link: https://bit.ly/470zRrO
Abstract:
Constructive logic is a generalisation of classical logic that applies in more situations, including mathematical universes (toposes) where propositions can take different values at different locations in some space or where every function from N to N is computable. Unfortunately, in this general setting many classical results of point-set topology fail. However, almost all of these results can be recovered if we reformulate topology in terms of lattices of opens without predefined underlying sets of points. Moreover, this perspective also sheds light on many not-obviously-topological aspects of constructive mathematics itself.
In this third lecture, Graham will describe the construction of free frames and introduce sublocales. Along the way we will also see that finiteness can be quite subtle in constructive mathematics, but can be understood by analogy to some topological concepts.
Speaker Bio:
Graham Manuell is a lecturer at Stellenbosch University. His research interests include pointfree topology, category theory, constructive mathematics and semigroup theory.
Graham Manuell (Aug 26 2024 at 14:13):The above times are GMT+2, so -.
Roy Ferguson (Sep 02 2024 at 12:59):Hello! Graham will be continuing the workshop series on pointfree topology and constructive mathematics next Tuesday. The details are as follows.
Speaker: Graham Manuell
Title: Workshop on pointfree topology and constructive mathematics - part 4
Date and time: -
Zoom registration link: https://bit.ly/3z749N6
Abstract:
Constructive logic is a generalisation of classical logic that applies in more situations, including mathematical universes (toposes) where propositions can take different values at different locations in some space or where every function from N to N is computable. Unfortunately, in this general setting many classical results of point-set topology fail. However, almost all of these results can be recovered if we reformulate topology in terms of lattices of opens without predefined underlying sets of points. Moreover, this perspective also sheds light on many not-obviously-topological aspects of constructive mathematics itself.
In the penultimate lecture of the series, we will cover Hausdorffness, discreteness, compactness, overtness. These have elegant logical formulations in terms of equality in, and quantification over, locales.
Roy Ferguson (Sep 09 2024 at 13:31):Hello! Graham will be concluding the workshop series on pointfree topology and constructive mathematics tomorrow. The details are as follows.
Speaker: Graham Manuell
Title: Workshop on pointfree topology and constructive mathematics - part 5
Date and time: -
Zoom registration link: https://bit.ly/3AWZu10
Abstract:
Constructive logic is a generalisation of classical logic that applies in more situations, including mathematical universes (toposes) where propositions can take different values at different locations in some space or where every function from N to N is computable. Unfortunately, in this general setting many classical results of point-set topology fail. However, almost all of these results can be recovered if we reformulate topology in terms of lattices of opens without predefined underlying sets of points. Moreover, this perspective also sheds light on many not-obviously-topological aspects of constructive mathematics itself.
In this final lecture we will discuss how many apparently nonconstructive results remain true constructively if phrased in terms of locales and give an example application of constructive pointfree topology to classical topology.