BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jaco Ruit (Utrecht University) DTSTART:20241115T090000Z DTEND:20241115T103000Z DTSTAMP:20260422T155204Z UID:HKUST-AG/64 DESCRIPTION:Title: On the theory of double $\\infty$-categories II\nby Jaco Ruit (Utrec ht 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 a ims to give a detailed introduction to double $\\infty$-categories. Double $\\infty$-categories can be viewed as generalizations of $(\\infty\,2)$-c ategories that admit two directions for morphisms. The series starts by mo tivating these categorical constructions\, and we will see how these appea r in mathematics. We will discuss their definitions\, including different completeness assumptions. Moreover\, we will see how double $\\infty$-cate gories can be used to model $(\\infty\,2)$-categories. We highlight some important examples of double $\\infty$-categories throughout.\n\nWe will t hen continue to study the notions of companionships and conjunctions in do uble $\\infty$-categories. These are important and useful concepts that ca n be used to describe the universal property of so-called squares construc tions\, as we will see. Moreover\, we will study functors between double $ \\infty$-categories and show that they assemble into double $\\infty$-cate gories of functors with vertical and horizontal natural transformations. W e present a new result that characterizes the companions and conjoints in these functor double $\\infty$-categories. On the way\, we will see how th is double categorical machinery can be specialized to prove results in $(\ \infty\,2)$-category theory.\n\nDuring the first talk\, we will recall som e relevant background material on $\\infty$-categories that will be needed to follow the series. No knowledge of $(\\infty\,2)$-categories is assume d.\n\nLecture series: On the theory of double $\\infty$-categories\n LOCATION:https://researchseminars.org/talk/HKUST-AG/64/ END:VEVENT END:VCALENDAR