0 A relative Yoneda Lemma

A Relative Yoneda Lemma (manuscript) a Remark of the Referee

We construct set-valued right Kan extensions via a relative Yoneda Lemma. As the referee pointed out, (2.1) 'can essentially be found in much greater generality' in Therefore, we withdraw this note as a preprint. Since (2.1, 3.1) might be of some use for the working mathematician, we leave it accessible as a manuscript. In using (2.1), the reader should refer to [Ke 82], in using (3.1), he shou...

Implications of Yoneda Lemma to Category Theory

This is a survey paper on the implication of Yoneda lemma, named after Japanese mathematician Nobuo Yoneda, to category theory. We prove Yoneda lemma. We use Yoneda lemma to prove that each of the notions universal morphism, universal element, and representable functor subsumes the other two. We prove that a category is anti-equivalent to the category of its representable functors as a corollar...

Ext A LA YONEDA WITHOUT THE SCHANUEL LEMMA

By means of a more precise treatment of the congruence relation between n-extensions we show that it is possible to avoid the Schanuel Lemma for proving some results on the functors Ext. An n-extension E from D to C is an exact sequence of the form (1) 0 C El E2 * * En D 0 in an abelian category. The idea to use congruence classes n-extensions as elements of Ext' (D C) is due to Yoneda ([7], [8...

On the Completion Monad via the Yoneda Embedding in Quasi-uniform Spaces

Making use of the presentation of quasi-uniform spaces as generalised enriched categories, and employing in particular the calculus of modules, we define the Yoneda embedding, prove a (weak) Yoneda Lemma, and apply them to describe the Cauchy completion monad for quasi-uniform spaces.

2-Categories and Yoneda lemma