In their 1967 book "Calculus of Fractions and Homotopy Theory", P.

Gabriel and M. Zisman introduced calculus of fractions as a tool for

understanding the localization of a category at a class of weak

equivalences. While powerful, the condition of calculus of fractions is

quite restrictive and it is rarely satisfied in various homotopical

settings, like model categories or Brown's categories of fibrant

objects, where one instead has *homotopy* calculus of fractions.

This talk is based on joint work with D. Carranza and Z. Lindsey, which

aims to reconcile the two. We define calculus of fractions for

quasicategories and give a workable model for the localization of a

marked quasicategory satisfying our condition. Although we have already

found several applications of this result, I would be very interested in

getting feedback from the audience and exploring new applications.

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# Higher-dimensional Calculus of Fractions

Chris Kapulkin (Western Ontario)

Thursday, April 27, 2023 - 2:00pm to 3:00pm

PDL C-401