BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michael Shulman (University of San Diego) DTSTART:20200422T170000Z DTEND:20200422T180000Z DTSTAMP:20260423T024445Z UID:ACTUCR/2 DESCRIPTION:Title: S tar-autonomous envelopes\nby Michael Shulman (University of San Diego) as part of ACT@UCR\n\n\nAbstract\nSymmetric monoidal categories with dual s\, a.k.a. compact monoidal categories\, have a pleasing string diagram ca lculus. In particular\, any compact monoidal category is closed with $[A\ ,B] = (A^* \\otimes B)$\, and the transpose of $A \\otimes B \\to C$ to $A \\to [B\,C]$ is represented by simply bending a string. Unfortunately\, a closed symmetric monoidal category cannot even be embedded fully-faithfu lly into a compact one unless it is traced\; and while string diagram calc uli for closed monoidal categories have been proposed\, they are more comp licated\, e.g. with "clasps" and "bubbles". In this talk we obtain a stri ng diagram calculus for closed symmetric monoidal categories that looks al most like the compact case\, by fully embedding any such category in a sta r-autonomous one (via a functor that preserves the closed structure) and u sing the known string diagram calculus for star-autonomous categories. No knowledge of star-autonomous categories will be assumed.\n LOCATION:https://researchseminars.org/talk/ACTUCR/2/ END:VEVENT END:VCALENDAR