An Adjoint Characterization of the Category of Sets (1994) [6 citations — 2 self]
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author = {Robert Rosebrugh and R. J. Wood},
title = {An Adjoint Characterization of the Category of Sets},
journal = {Proc. Amer. Math. Soc},
year = {1994},
volume = {122},
pages = {409--413}
}
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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 on foundations and our notation is necessary. We write set for the category of small sets and assume that there is a Grothendieck topos, SET, of sets which contains the set of arrows of set as an object. The 2-category of category objects in SET, which we write CAT, is cartesian closed and set is an object of CAT. Thus, for C a category in CAT, CAT(C op ; set) is also an object of CAT and we abbreviate it by MC; (it was written PC in [8].) Substitution gives a 2-functor M : CAT coop \Gamma...
Citations
| 26 | Yoneda structures on 2-categories – Street, Walters - 1978 |
| 14 | Boundedness and complete distributivity – Rosebrugh, Wood |
| 7 | Constructive complete distributivity IV – Rosebrugh, Wood - 1994 |
| 3 | L'egitimit'e des cat'egories de pr'efaisceaux, Diagrammes 1 – Foltz - 1979 |
| 2 | Idempotents in bicategories – Par'e, Rosebrugh, et al. - 1989 |
| 2 | Some remarks on total categories – Wood - 1982 |
| 1 | Notions of topos – Street - 1981 |
| 1 | Unpublished manuscript – Street - 1979 |
