Final lift actions associated with topological functors

Research output: Contribution to journalArticle

Abstract

For a topological functor U : E → B, the fiber U-1(b), b ∈ B, is a cocomplete poset and the left action, induced by final lift, of the endomorphism monoid B(b, b) on U-1 (b) is cocontinuous. It is shown that every cocontinuous left action of B(b, b) on any cocomplete poset can be realized as the final lift action associated to a canonically defined topological functor over B. If B is a Grothendieck topos and b = Ω, the subobject classifier, then B(Ω, Ω) inherits both a monoidal and a cocomplete poset structure. In the case B = Sets, all cocontinuous left actions of B(Ω, Ω) on itself are explicitly described and each is shown to arise as the final lift action associated to a specific subcategory of a certain fixed category, referred to as the category of LR-spaces. Relationships between these LR-spaces and several other well known topological categories are also considered.

Original languageEnglish (US)
Pages (from-to)495-504
Number of pages10
JournalApplied Categorical Structures
Volume10
Issue number5
DOIs
StatePublished - Oct 1 2002

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Functor
Poset
Topological Category
Classifiers
Topos
Endomorphism
Monoid
Fibers
Classifier
Fiber

Keywords

  • Final lift actions
  • Topological category

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Final lift actions associated with topological functors. / Mielke, Marvin.

In: Applied Categorical Structures, Vol. 10, No. 5, 01.10.2002, p. 495-504.

Research output: Contribution to journalArticle

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