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Yoneda structures from 2-toposes

Applied Categorical Structures, Vol. 15, p259-323, 2007

A 2-categorical generalisation of the notion of elementary topos is provided, and some of the properties of the yoneda structure [1] it generates are explored. Results enabling one to exhibit objects as cocomplete in the sense definable within a yoneda structure are presented. Examples relevant to the globular approach to higher dimensional category theory are discussed. This paper also contains some expository material on the theory of fibrations internal to a finitely complete 2-category [2] and provides a self-contained development
of the necessary background material on yoneda structures.

[1]  R. Street and R.F.C. Walters, Yoneda structures on 2-categories, J.Algebra 50 (1978), 350–379.
[2]  R. Street, Fibrations and yoneda’s lemma in a 2-category, Lecture Notes in Math. 420 (1974), 104–133
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  495k v. 1 Sep 25, 2009, 3:50 AM Mark Weber