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 language | English (US) |
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Pages (from-to) | 495-504 |
Number of pages | 10 |
Journal | Applied Categorical Structures |
Volume | 10 |
Issue number | 5 |
DOIs | |
State | Published - Oct 2002 |
Keywords
- Final lift actions
- Topological category
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)