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Equilogical spaces and algebras for a double-power monad

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The category Equ of equilogical spaces was introduced by Scott in 1996 and it provides a useful cartesian closed extension of the category of T_0 spaces and continuous maps. In this talk we will investigate the monad of the double power of the Sierpinski space on the category of equilogical spaces and we will analyse the algebras for this monad, pointing out a connection with the category of frames and frame homomorphisms. Moreover, we focus our attention on particular subcategories of Equ, we restrict the double-power monad to them and we investigate the algebras for this monad in these cases. In particular, we introduce a full subcategory REqu of Equ which turns out to be very relevant in the study of the double-power monad and we relate the algebras in this category with the category of sober spaces.

This talk is part of the Category Theory Seminar series.

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