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SIMBa: Topological models of ∞-groupoids

SIBMa

El proper dimecres, 3 de novembre, se celebrarà una nova xerrada —en format virtual i, alerta, presencial!— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: David Martínez Carpena
Universitat: Universitat de Barcelona

Data: Wednesday, November 3rd, 2021.
Hora: 12:00, coffee break; 12:20, talk.
Lloc: Zoom | Presencial: Aula B2
Idioma: English.

Títol: Topological models of ∞-groupoids
Resum: In higher category theory, ∞-groupoids are ∞-categories whose morphisms are weakly invertible at all orders. Every topological space has an associated ∞-groupoid, named its fundamental ∞-groupoid, which encodes the information of higher paths over the space. The statement that every space can be recovered up to homotopy from its fundamental ∞-groupoid is known as Grothendieck’s homotopy hypothesis. In this presentation, we choose a model of ∞-categories based on topologically enriched categories, and discuss the homotopy hypothesis in this context.

 

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