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Completeness and cocompleteness of the categories of basic pairs and concrete spaces

Published online by Cambridge University Press:  10 November 2014

HAJIME ISHIHARA  and
TATSUJI KAWAI
HAJIME ISHIHARA
Affiliation:
School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan Email: ishihara@jaist.ac.jp and tatsuji.kawai@jaist.ac.jp
TATSUJI KAWAI
Affiliation:
School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan Email: ishihara@jaist.ac.jp and tatsuji.kawai@jaist.ac.jp
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Abstract

We show that the category of basic pairs (BP) and the category of concrete spaces (CSpa) are both small-complete and small-cocomplete in the framework of constructive Zermelo–Frankel set theory extended with the set generation axiom. We also show that CSpa is a coreflective subcategory of BP.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 25 , Special Issue 8: Computing with Infinite Data: Topological and Logical Foundations Part 2 , December 2015 , pp. 1626 - 1648
Copyright
Copyright © Cambridge University Press 2014 

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