# Questions tagged [yoneda-lemma]

The tag has no usage guidance.

34 questions
Filter by
Sorted by
Tagged with
504 views

252 views

### All functors "are" left adjoints, and applications?

Throughout this thread, let us assume smallness. All functors "are" left adjoints Let $D \xrightarrow{F} C$ be any functor, which induces $$D \xrightarrow{F} \hat{C}$$ by compositing the ...
363 views

### Is the Kolmogorov-Arnold representation theorem an example of the Yoneda lemma?

From Wikipedia: https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Arnold_representation_theorem In real analysis and approximation theory, the Kolmogorov–Arnold representation theorem (or ...
196 views

### How to learn about Higher Topoi

I have been learning quasicategory theory in an attempt to understand higher topoi, and I have been trying to look at as many different sources as possible. Higher Topos Theory provides a higher ...
235 views

### Is Cauchy completion the largest extension with the same free cocompletion?

EDIT Title has been edited. Let $C$ be a category, and $$\hat{C} = [C^{op}, (Set)]$$ be its free cocompletion. Despite its name, the free cocompletion of free cocompletion is not equivalent to the ...
380 views

### Yoneda lemma for monoidal categories

I am looking at the Yoneda lemma trying to see where the assumption of "locally small" really comes in. Obviously in order to define a functor to the category sets using $Hom$-spaces we need ...
138 views

### Does Cantor Bernstein hold in a Closed Symmetric Monoidal Category?

In a closed symmetric monoidal category with $[I,X] \cong X$ for all $X$ is it true that having monomorphisms $m :A \rightarrow B$ and $m: B \rightarrow A$ is enough to imply $A \cong B$ ? I tried to ...
341 views

422 views

### Basic category theory: Universality of adjunction unit is justified by Yoneda Proposition in Mac Lane's text [closed]

Background I am reviewing some category theory, which I did not learn too well the first time around. One text I am using is Mac Lane's. Near the beginning of the chapter on adjunctions (pg 80), he ... 442 views

359 views

### Given a small category with some colimits, can the rest of the colimits be added?

Let $\mathcal{A}$ be a small category with some ( maybe no) colimits. What I would like to be able to do is add the rest of the colimits in a universal way. The Yoneda lemma will not work, since this ...