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Abstract Sobriety and Equilogical Spaces

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If you have a question about this talk, please contact Guilherme Lima de Carvalho e Silva.

Sobriety is a topological property, identifying those spaces which are completely determined by (the frame structure of) their topology. This notion will be introduced focusing on its category-theoretic properties, and in particular by making use of the language of monads and algebras.

Recently (2002) Paul Taylor has proposed the notion of abstract sobriety, generalising that of sobriety to a categorical setting. It will be shown in which regard the new definition is an extension of the standard one, as well as some of its properties.

Finally the notion of abstract sobriety will be applied to the category of equilogical spaces, a cartesian closed extension of Top. In this setting the notions of standard and abstract sobriety coincide, while other properties seem more problematic.

This talk is part of the Junior Category Theory Seminar series.

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