BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Juan F. Meleiro DTSTART:20220518T160000Z DTEND:20220518T170000Z DTSTAMP:20260423T053046Z UID:EmCats/8 DESCRIPTION:Title: T owards Modular Mathematics\nby Juan F. Meleiro as part of Em-Cats\n\n\ nAbstract\nSynthetic Reasoning is a style of mathematics based on axiomati c theories that aim to capture the fundamental and essential structures in a particular subject. Such theories are often type theories with intended interpretations inside structured categories such as toposes.\n\nBut theo rycrafting is currently an artisanal job\, that requires analysis and synt hesis from scratch for every theory that will be created. A formal (and ca tegorical) toolkit for manipulating these theories could aid the synthetic mathematician in their endeavors\, just as a toolbox can help any artisan in their craft.\n\nModular mathematics is mathematics based on these form al theories that capture a way of Synthetic Reasoning in particular fields \, and can then be combined and compared. In this talk\, I will present wo rk in progress towards a framework for such modular mathematics. Universal Logic will be our guide for the capabilities that such a framework should provide\, including translation between\, and combinations of theories. I will present a formal theory called MMT (introduced by Florian Rabe) that follows such a guide. I will then present three formal approaches to the definition of the fundamental group\, each following a distinct style: a p urely categorical\, a syntactical-categorical\, and a purely syntactical o ne\; all in order to explore some possible ways to do Modular Mathematics. \n LOCATION:https://researchseminars.org/talk/EmCats/8/ END:VEVENT END:VCALENDAR