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Yoneda Structures from 2-toposes

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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.

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  1. Department of Mathematics, Division of ICS, Macquarie University, Sydney, NSW, 2109, Australia

    Mark Weber

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Weber, M. Yoneda Structures from 2-toposes. Appl Categor Struct 15, 259–323 (2007). https://doi.org/10.1007/s10485-007-9079-2

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