Professor of Mathematics, University of Genoa

Remarks About Equilogical Spaces

Abstract:

Equilogical spaces were introduced by Dana Scott in his seminal paper on Data

Types as Lattices as a "good category of spaces for computation". We shall

review the presentation of the category of equilogical spaces and present two

applications to logic. The first is that it subsumes a model for Martin-Loef

Type Theory where to discuss the univalent axiom with respect to topological

spaces. The second is to give a synthetic presentation of the category of

frames which suggest that frames are algebras for geometric logic.

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