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UID:4b0e414bc3572c39ed4a7466d4a673f1
CATEGORIES:Colloquia
CREATED:20230926T102316
SUMMARY:Do we need a new foundation for higher structures?
LOCATION:Hill 705
DESCRIPTION:<p>Emily Riehl (Johns Hopkins U.)</p><p>Title: Do we need a new foundation 
 for higher structures?</p><p>Abstract: The fundamental theorem of category 
 theory is the Yoneda lemma, which in its simplest form identifies natural t
 ransformations between represented functors with morphisms between the repr
 esenting objects. The ?-categorical Yoneda lemma is surprisingly hard to pr
 ove --- at least in the traditional set-based foundations of mathematics. I
 n this talk we'll describe the experience of developing ?-category theory i
 n an alternate foundation system based on homotopy type theory, in which co
 nstructions determined up to a contractible space of choices are genuinely 
 "well-defined" and elementwise mappings are automatically homotopically-coh
 erently functorial. In this setting, the proof the ?-categorical Yoneda lem
 ma is arguably easier than the 1-categorical Yoneda lemma. We'll end by pos
 ing the question as to whether similar foundations would be useful for othe
 r "higher structures." This is based on joint work with Mike Shulman and in
 volves computer formalizations written in collaboration with Nikolai Kudaso
 v and Jonathan Weinberger.</p><p>&nbsp;</p>
CONTACT:Emily Riehl
DTSTAMP:20260830T202514
DTSTART;TZID=America/New_York:20231004T153000
DTEND;TZID=America/New_York:20231004T163000
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