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Completions of Ordered Sets

Published online by Cambridge University Press:  20 November 2018

B. T. Ballinger
B. T. Ballinger*
Affiliation:
McGill University, Montreal, Quebec
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Completions of categories were studied by Lambek in [3], using the contravariant Horn functor to embed a small category C into the functor category (C*, S), where C* is the opposite category of C, and S is the category of sets. Three completions of C were considered; the completion (C*, S), the full subcategory (C*, C)inf⊆(C*, S) whose objects consist of all inf-preserving functors, and the full sub-category B⊆(C*, S)inf consisting of all subobjects of products of representable functors of the form HomC(—, C), C an object of C.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 4 , December 1972 , pp. 469 - 472
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Banaschewski, B., Hüllensysteme und Erweiterung von Quasi-Ordnungen, Z. Math. Logik Grundlagen Math. 2 (1956), 117-130.Google Scholar
2. Birkhoff, G., Lattice theory, Colloq. Publ., Vol. 25, Amer. Math. Soc, Providence, R.I., 1967.Google Scholar
3. Lambek, J., Completions of categories, Springer Lecture Notes in Mathematics 24, 1966.Google Scholar
4. Mitchell, B., Theory of categories, Academic Press, New York, 1965.Google Scholar