Well, I remember encountering this Yoneda Lemma somewhere in a class I had on category theory the first year, which at the time I did not follow very well, and still do not, since I was thrown off track by another theorem: Antoine’s Extension Theorem which implies that though there are nice embeddings in which the original space is recoverable (by complementation-cohomology) from the embedded object (and vice versa), there are cases where this cannot happen, as in various types of knots and links. Does any of this ring a bell or conflict-generalize what the Yoneda Lemma says?