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Applied Categorical Structures

, Volume 15, Issue 3, pp 259–323 | Cite as

Yoneda Structures from 2-toposes

  • Mark WeberEmail author
Article
First Online:

Abstract

A 2-categorical generalisation of the notion of elementary topos is provided, and some of the properties of the Yoneda structure (Street and Walters, J. Algebra, 50:350–379, 1978) 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 (Street, Lecture Notes in Math., 420:104–133, 1974) and provides a self-contained development of the necessary background material on Yoneda structures.

Keywords

2-topos Fibration Yoneda structure Internal category theory 

Mathematics Subject Classifications (2000)

18A05 18A15 18B25 18D05 
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© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Mathematics, Division of ICSMacquarie UniversitySydneyAustralia

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