Yoneda completeness

0 A relative Yoneda Lemma

We construct set-valued right Kan extensions via a relative Yoneda Lemma.

2-Categories and Yoneda lemma

Normalization and the Yoneda Embedding

Received We show how to solve the word problem for simply typed-calculus by using a few well-known facts about categories of presheaves and the Yoneda embedding. The formal setting for these results is P-category theory, a version of ordinary category theory where each hom-set is equipped with a partial equivalence relation. The part of P-category theory we develop here is constructive and thus...

Yoneda Structures from 2-toposes

A 2-categorical generalisation of the notion of elementary topos is provided, and some of the properties of the yoneda structure [SW78] 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 cont...

Higher Extension Modules and the Yoneda Product

Abstract. A chain of c submodules E =: E0 ≥ E1 ≥ · · · ≥ Ec ≥ Ec+1 := 0 gives rise to c composable 1-cocycles in Ext1(Ei−1/Ei, Ei/Ei+1), i = 1, . . . , c. In this paper we follow the converse question: When are c composable 1-cocycles induced by a module E together with a chain of submodules as above? We call such modules c-extension modules. The case c = 1 is the classical correspondence betwe...