We analyse the category-theoretical structures involved with the notion of continuity within the framework of formal topology. We compare the category of basic pairs to other categories of "spaces" by means of canonically determined functors and show how the definition of continuity is determined in a certain, canonical sense. Finally, we prove a standard adjunction between the (co)algebraic approach to spaces and the category of topological spaces.

Completions, comonoids, and topological spaces / A. Bucalo, G. Rosolini. - In: ANNALS OF PURE AND APPLIED LOGIC. - ISSN 0168-0072. - 137:1-3(2006 Jan), pp. 104-125.

Completions, comonoids, and topological spaces

A. Bucalo;
2006

Abstract

We analyse the category-theoretical structures involved with the notion of continuity within the framework of formal topology. We compare the category of basic pairs to other categories of "spaces" by means of canonically determined functors and show how the definition of continuity is determined in a certain, canonical sense. Finally, we prove a standard adjunction between the (co)algebraic approach to spaces and the category of topological spaces.
Category theory; Commutative comonoid; Complete sup-lattice; Regular completion
Settore MAT/01 - Logica Matematica
Article (author)
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/14409
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 3
social impact