Geodesic
Completions of Ordered Sets
Canadian mathematical bulletin, Tome 15 (1972) no. 4, pp. 469-472

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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. 
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
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     title = {Completions of {Ordered} {Sets}},
     journal = {Canadian mathematical bulletin},
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     year = {1972},
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     number = {4},
     doi = {10.4153/CMB-1972-084-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-084-2/}
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