Presenting Locale Pullback Via Directed Complete Posets | Zendy

Christopher Townsend | Zendy

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Presenting Locale Pullback Via Directed Complete Posets

Author(s) -

Christopher Townsend

Publication year - 2004

Publication title -

electronic notes in theoretical computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.242

H-Index - 60

ISSN - 1571-0661

DOI - 10.1016/j.entcs.2004.08.013

Subject(s) - pullback , locale (computer software) , morphism , mathematics , pure mathematics , frame (networking) , algebra over a field , computer science , programming language , telecommunications

This paper shows how to describe the pullbacks of directed complete posets (dcpos) along geometric morphisms. This extends Joyal and Tierney’s original results on the pullbacks of suplattices. It is then shown how to treat every frame as a dcpo and so locale pullback is described in this way. Applications are given describing triquotient assignments in terms of internal dcpo maps, leading to pullback stability results for triquotient maps. The main application here shows how dcpo maps between frames can be described in terms of certain external natural transformations.

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