BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jaco Ruit (Utrecht University) DTSTART:20241113T084500Z DTEND:20241113T094500Z DTSTAMP:20260422T161047Z UID:HKUST-AG/61 DESCRIPTION:Title: On the theory of double $\\infty$-categories I\nby Jaco Ruit (Utrech t University) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture h eld in Room 4475 (Lifts 25/26).\n\nAbstract\nThis series of three talks ai ms to give a detailed introduction to double $\\infty$-categories. Double $\\infty$-categories can be viewed as generalizations of $(\\infty\,2)$-ca tegories that admit two directions for morphisms. The series starts by mot ivating these categorical constructions\, and we will see how these appear in mathematics. We will discuss their definitions\, including different c ompleteness assumptions. Moreover\, we will see how double $\\infty$-categ ories can be used to model $(\\infty\,2)$-categories. We highlight some i mportant examples of double $\\infty$-categories throughout.\n\nWe will th en continue to study the notions of companionships and conjunctions in dou ble $\\infty$-categories. These are important and useful concepts that can be used to describe the universal property of so-called squares construct ions\, as we will see. Moreover\, we will study functors between double $\ \infty$-categories and show that they assemble into double $\\infty$-categ ories of functors with vertical and horizontal natural transformations. We present a new result that characterizes the companions and conjoints in t hese functor double $\\infty$-categories. On the way\, we will see how thi s double categorical machinery can be specialized to prove results in $(\\ infty\,2)$-category theory.\n\nDuring the first talk\, we will recall some relevant background material on $\\infty$-categories that will be needed to follow the series. No knowledge of $(\\infty\,2)$-categories is assumed .\n\nLecture series: On the theory of double $\\infty$-categories\n LOCATION:https://researchseminars.org/talk/HKUST-AG/61/ END:VEVENT END:VCALENDAR