Completions of Ordered Sets
Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 469-472
Voir la notice de l'article provenant de la source Cambridge University Press
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.
Ballinger, B. T. Completions of Ordered Sets. Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 469-472. doi: 10.4153/CMB-1972-084-2
@article{10_4153_CMB_1972_084_2,
author = {Ballinger, B. T.},
title = {Completions of {Ordered} {Sets}},
journal = {Canadian mathematical bulletin},
pages = {469--472},
year = {1972},
volume = {15},
number = {4},
doi = {10.4153/CMB-1972-084-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-084-2/}
}
[1] 1. Banaschewski, B., Hüllensysteme und Erweiterung von Quasi-Ordnungen, Z. Math. Logik Grundlagen Math. 2 (1956), 117-130. Google Scholar
[2] 2. Birkhoff, G., Lattice theory, Colloq. Publ., Vol. 25, Amer. Math. Soc, Providence, R.I., 1967. Google Scholar
[3] 3. Lambek, J., Completions of categories, Springer Lecture Notes in Mathematics 24, 1966. Google Scholar
[4] 4. Mitchell, B., Theory of categories, Academic Press, New York, 1965. Google Scholar
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