The paper analyses the category-theoretical structures involved with the notion of continuity in the framework of formal topology. It contains a comparison of the category of basic pairs with other categories of “spaces” by means of canonically determined functors and shows how the definition of continuity is determined in a certain, canonical sense. Finally, a standard adjunction is constructed between the (co)algebraic approach to spaces and the category of topological spaces.
Completions, comonoids, and topological spaces
ROSOLINI, GIUSEPPE
2006-01-01
Abstract
The paper analyses the category-theoretical structures involved with the notion of continuity in the framework of formal topology. It contains a comparison of the category of basic pairs with other categories of “spaces” by means of canonically determined functors and shows how the definition of continuity is determined in a certain, canonical sense. Finally, a standard adjunction is constructed between the (co)algebraic approach to spaces and the category of topological spaces.
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