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Seminar

HC - (infinity,2)-categories Working Group: The Gray tensor product for 2-quasi-categories February 19, 2020 (10:00 AM PST - 11:30 AM PST)
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Location: MSRI: Simons Auditorium
Speaker(s) Yuki Maehara (Macquarie University)
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The (lax) Gray tensor product (or more accurately its associated closed structure) plays a crucial role in, among other things, Street's formal theory of monads. The goal of this talk is to homotopify the statement "the Gray tensor product forms part of a monoidal closed structure on 2-Cat" into a 2-quasi-categorical version, with an eye towards developing the formal theory of homotopy coherent monads.

The first half of the talk will be devoted to describing the main combinatorial tool I used to prove this result, namely Oury's inner horns. These horns provide a combinatorially tractable characterisation of Ara's model structure.

 

Bibliography:

Dimitri Ara. Higher quasi-categories vs higher Rezk spaces. Journal of K-Theory. K-Theory and its Applications in Algebra, Geometry, Analysis & Topology, 14(3):701, 2014.

John W. Gray. Formal category theory: adjointness for 2-categories. Lecture Notes in Mathematics, Vol. 391. Springer-Verlag, Berlin-New York, 1974.

David Oury. Duality for Joyal’s category Θ and homotopy concepts for Θ_2-sets. PhD thesis, Macquarie University, 2010.

Ross Street. The formal theory of monads. J. Pure Appl. Algebra, 2(2):149–168, 1972.

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