Dialectica Comonoids (Valeria de Paiva at University of Denver Algebra and Logic Seminar 2023)
Channel: Charlotte Aten
Date: 2023-03-18

This is from my old YouTube channel. My new channel can be found at https://www.youtube.com/@CharlotteAten

This is a talk that Valeria de Paiva gave for the University of Denver Algebra and Logic Seminar in the winter of 2023. She told us about comonoids as they appear in both the Dialectica construction as well as elsewhere in mathematics. Her abstract and some useful links appear below.

Title: Dialectica Comonoids
Speaker: Valeria de Paiva, Topos Institute
Abstract: The Dialectica construction (Goedel 1958) is a proof-theoretical construction that has found many applications in recent theoretical Computer Science, via its categorical explanation (de Paiva 1989 and many others). Comonoids, unlike monoids that everyone learns in the first courses in Algebra, seem a bit unusual and not very useful. This talk wants to show that comonoids are useful and not only in conjunction with dialectica categories.

Slides: https://aten.cool/documents/DenverComonoids2023.pdf
Valeria de Paiva: https://vcvpaiva.github.io/
Topos Institute: https://topos.institute/
Special Session on Applied Category Theory at JMM 2023: https://sites.google.com/view/jmm2023-special-session-act/