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Pointless spaces: Frames and their uses in Algebra and Topology

Thursday, September 5, 13:00 hrs.

Luis Ángel Zaldívar Corichi

Universidad de Guadalajara, Mexico

Abstract: A frame (locale, complete heyting algebra) consist of a complete lattice

(A,≤, V, ∧,0,1)

in which the following distributive law holds:

α(VX) = V{αx | xX },

for everyXA and αA. Frames are, in specific ways, algebraic manifestations of topological spaces. The ubiquitous example of a frame is the frame of opens of any topological space.

In this talk, we will see that in many algebraic phenomena there is a frame that controls certain process, (for instance the localizations of any Grothendieck category constitutes a frame), more over the point-free aspects of these frames served as a classification devices for many algebraic and topological situations.

Semblance: He obtained his doctorate at UNAM under the tutelage of Professor Jose Ríos Montes. Former FulBright Scholar Garcia Robles 2017-2018. Since 2019, he has been a full-time professor in the Mathematics Department of the University of Guadalajara. His research areas range between Abelian categories, module categories, tensor triangulated categories, and poin-free topology and its interaction between them.