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Abstract: If a category B with Yoneda embedding Y : B \Gamma! CAT(B op ; set) has an adjoint string, U a V a W a X a Y; then B is equivalent to set. The authors gratefully acknowledge financial support from NSERC Canada. Diagrams typeset using M. Barr's diagram macros. 1 Introduction The statement of the Abstract was implicitly conjectured in [9]. Here we establish the conjecture. We will see that it suffices to assume that B has an adjoint string V a W a X a Y with V pullback preserving. A word ... (Update)
Context of citations to this paper: More
...and sent him our proof. This was reported in [F2] but our proof was still not published. Now that there is actually an application [RW], we decided publication was in order. We have expressed the construction in a form we believe begs generalization to, for example,...
.... most physical of all the objects of traditional concrete (set based) mathematics, if not of all category theory (and perhaps even there, cf. [RW94]) Set op is equivalent to the category of complete atomic Boolean algebras (CABA s) But the free CABA generated by the set X is...
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2: Algebraic and Topological Representations of Groups (context) - Pultr, Trnkov'a - 1980
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BibTeX entry: (Update)
Robert Rosebrugh and Richard Wood, An adjoint characterization of the category of sets, Proceedings AMS 122 (1994) 409-413. http://citeseer.ist.psu.edu/rosebrugh94adjoint.html More
@article{ rosebrugh94adjoint,
author = "Rosebrugh, R. and Wood, R.J.",
title = "An adjoint characterization of the category of sets",
journal = "Proc. Amer. Math. Soc.",
volume = "122",
number = "2",
pages = "409-413",
year = "1994",
url = "citeseer.ist.psu.edu/rosebrugh94adjoint.html" }
Citations (may not include all citations):15 Yoneda structures on 2-categories (context) - Street, Walters - 1978
12 Harper and Row (context) - Freyd - 1964
11 Constructive complete distributivity (context) - Fawcett, Wood - 1990
8 Constructive complete distributivity IV - Rosebrugh, Wood - 1992
2 Bulletin of the Australian Math (context) - Par'e, Rosebrugh et al. - 1989
2 Some remarks on total categories (context) - Wood - 1982
1 Unpublished manuscript (context) - Street - 1979
1 L'egitimit'e des cat'egories de pr'efaisceaux (context) - Foltz - 1979
1 Bulletin of the Australian Math Society (context) - Street, topos - 1981
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