BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jean-Simon Lemay DTSTART:20250612T170000Z DTEND:20250612T180000Z DTSTAMP:20260407T214207Z UID:ToposInstituteColloquium/201 DESCRIPTION:Title: Cartesian Fermat Categories\, a new class of Cartesian Differential Categories\nby Jean-Simon Lemay as part of Topos Institut e Colloquium\n\n\nAbstract\nCartesian differential categories (introduced by Blute\, Cockett\, and Seely) provide a categorical framework for diffe rential calculus\, and also provide the categorical foundations for the di fferential lambda calculus\, differentiable programming\, and certain auto matic differentiation techniques used for machine learning. Another approa ch to the categorical foundations of differentiation are Fermat theories ( introduced by Dubuc and Kock)\, which are Lawvere theories that have Hadam ard’s Lemma as an axiom. It is already known that every Fermat theory is a Cartesian differential category. However\, the definition of a Fermat t heory is heavily dependent on 1) being a Lawvere theory and 2) being able to multiply maps\, which are two things that are not assumed for Cartesian differential categories. In this talk\, we will introduce Cartesian Ferma t categories\, the proper Fermat theory analogue of a Cartesian differenti al category\, with the main result being that Cartesian Fermat category is a Cartesian differential category. This talk will also include a friendly introduction to Cartesian differential categories\, and thus will be acce ssible to anyone\, including newcomers\, interested in differential catego ries.\n\nThis talk is based on joint work with Carlos Pascual Miralles.\n LOCATION:https://researchseminars.org/talk/ToposInstituteColloquium/201/ END:VEVENT END:VCALENDAR