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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

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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.

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