BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jaco Ruit (Utrecht University) DTSTART:20241120T084500Z DTEND:20241120T094500Z DTSTAMP:20260422T161047Z UID:HKUST-AG/63 DESCRIPTION:Title: On the theory of double $\\infty$-categories III\nby Jaco Ruit (Utre cht University) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 4475 (Lifts 25/26).\n\nAbstract\nThis series of three talks aims to give a detailed introduction to double $\\infty$-categories. Doubl e $\\infty$-categories can be viewed as generalizations of $(\\infty\,2)$- categories that admit two directions for morphisms. The series starts by m otivating these categorical constructions\, and we will see how these appe ar in mathematics. We will discuss their definitions\, including different completeness assumptions. Moreover\, we will see how double $\\infty$-cat egories can be used to model $(\\infty\,2)$-categories. We highlight some important examples of double $\\infty$-categories throughout.\n\nWe will then continue to study the notions of companionships and conjunctions in d ouble $\\infty$-categories. These are important and useful concepts that c an be used to describe the universal property of so-called squares constru ctions\, as we will see. Moreover\, we will study functors between double $\\infty$-categories and show that they assemble into double $\\infty$-cat egories of functors with vertical and horizontal natural transformations. We present a new result that characterizes the companions and conjoints in these functor double $\\infty$-categories. On the way\, we will see how t his double categorical machinery can be specialized to prove results in $( \\infty\,2)$-category theory.\n \nDuring the first talk\, we will recall s ome relevant background material on $\\infty$-categories that will be need ed to follow the series. No knowledge of $(\\infty\,2)$-categories is assu med.\n\nLecture series: On the theory of double $\\infty$-categories\n LOCATION:https://researchseminars.org/talk/HKUST-AG/63/ END:VEVENT END:VCALENDAR