The Yoneda Embedding is Injective on Isomorphism Classes

Let $latex \mathcal{A}$ be a locally small category. We say that the Yoneda embedding of $latex \mathcal{A}$ is the functor: $latex H_\cdot:\mathcal{A} \rightarrow [\mathcal{A}^{op}, \mathbf{Set}]$. Now let $latex A, A' \in \mathcal{A}$ and suppose that $latex H_A \cong H_{A'}$. We aim to show that this means $latex A \cong A'$. By the definition of \$latex H_A, … Continue reading The Yoneda Embedding is Injective on Isomorphism Classes