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Title of Journal: Appl Categor Struct

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Abbravation: Applied Categorical Structures

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Springer Netherlands

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10.1002/hc.10016

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1572-9095

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Lawvere Completeness in Topology

Authors: Maria Manuel Clementino Dirk Hofmann
Publish Date: 2008/08/08
Volume: 17, Issue: 2, Pages: 175-210
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Abstract

It is known since 1973 that Lawvere’s notion of Cauchycomplete enriched category is meaningful for metric spaces it captures exactly Cauchycomplete metric spaces In this paper we introduce the corresponding notion of Lawvere completeness for mathbbTmathsfVcategories and show that it has an interesting meaning for topological spaces and quasiuniform spaces for the former ones it means weak sobriety while for the latter it means Cauchy completeness Further we show that mathsfV has a canonical mathbbTmathsfVcategory structure which plays a key role it is Lawverecomplete under reasonable conditions on the setting this structure permits us to define a Yoneda embedding in the realm of mathbbTmathsfVcategories

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Other Papers In This Journal:
  1. On the Notion of a Semi-Abelian Category in the Sense of Palamodov
  2. Complexity Analysis via Approach Spaces
  3. Axioms for Sequential Convergence
  4. A Categorical Foundation for Bayesian Probability
  5. Quasi Left Factorization Structures as Presheaves
  6. Absolute Lax 2-categories
  7. Auslander–Buchweitz Context and Co- t -structures
  8. Homotopy Gerstenhaber Structures and Vertex Algebras
  9. Perfect MV -algebras and their Logic
  10. Insertion of Continuous Real Functions on Spaces, Bispaces, Ordered Spaces and Pointfree Spaces—A Common Root
  11. A Generalization of De Vries Duality Theorem
  12. Bounded Equivalence of Hull Classes in Archimedean Lattice-Ordered Groups with Unit
  13. Normal Subgroups of B u Aut(Ω)
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