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Geometry-Topology Seminar

Thursday, April 25, 2019 - 4:30pm

Emily Riehl

Johns Hopkins University


University of Pennsylvania


Homotopical categories are designed to accommodate a more flexible notion of “sameness” between mathematical objects, relaxing “isomorphic” to “weakly equivalent.” This talk will survey a half century of work to extend ordinary category theory to this setting. We’ll introduce Gabriel and Zisman’s category of fractions and Dwyer and Kan’s hammock localization before turning our attention to the main players: Quillen’s model categories and the more modern (∞,1)-categories that have recently proliferated. No prior acquaintance with any of these topics will be assumed, and more details can be found in a paper with the same title on the arXiv.