Questions tagged [yoneda-lemma]

The Yoneda Lemma is a simple result of category theory, and its proof is very straightforward. Yet I feel like I do not truly understand what it is about; I have seen a few comments here mentioning ...

I'm looking for a reference explaining under what conditions the internal Yoneda lemma holds; in particular, I am wondering if it is known what properties of the ($2$-)category of categories are ...

Consider the definition of existence internal homs for a general monoidal category category $\cal{C}$, mainly the existence of an adjoint for the functor $$ X \otimes -: \cal{C} \to \cal{C}, $$ for ...

Let $\mathcal{C}$ and $\mathcal{D}$ be categories and let $T : \mathcal{C} \rightarrow \mathcal{D}$ be a functor. Suppose that $F : \mathcal{D}^\mathrm{op} \rightarrow \mathrm{Set}$ is a functor. (So ...

There is some discussion on the nLab on seeing the free cocompletion $\mathbf{Psh}(\mathbf{A}) = [\mathbf{A}^{op}, \mathbf{Sets}]$, as a pseudomonad. The Yoneda embedding $よ \colon \mathbf{A} \to \...