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SUMMARY:Kensuke Arakawa (Kyoto University)
DTSTART:20260421T230000Z
DTEND:20260422T003000Z
DTSTAMP:20260422T173343Z
UID:tandg/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/tandg/38/">O
 n the equivalence of two approaches to multiplicative homotopy theories</a
 >\nby Kensuke Arakawa (Kyoto University) as part of Topology and Geometry 
 Seminar (Texas\, Kansas)\n\n\nAbstract\nLocally presentable (\\infinity\,1
 ) categories admit two popular models: Presentable quasicategories and com
 binatorial model categories. Building on the foundational work of Dugger a
 nd Lurie\, Pavlov proved that their associated (\\infty\,1)-categories are
  equivalent\, confirming a long-standing expectation. He then went on to c
 onjecture that this should also hold multiplicatively\, i.e.\, for present
 ably symmetric monoidal quasicategories and combinatorial symmetric monoid
 al model categories. Such an equivalence would be of foundational importan
 ce in higher algebra.\n\nIn arXiv:2603.23018\, I proved this conjecture. T
 he main difficulty is that existing techniques to rigidify quasicategories
  often break down multiplicatively. In the talk\, I will explain how to ov
 ercome this. If time permits\, I will also explain applications to enriche
 d infinity operads (arXiv:2603.23019).\n
LOCATION:https://researchseminars.org/talk/tandg/38/
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