Matthew wrote:

> If so I think you mean "the *right* adjoint to \\( \Delta : \mathbf{Set} \to \mathbf{Set}^2 \\) is the product \\( \times : \mathbf{Set}^2 \to \mathbf{Set} \\)".

Yes, I wrote those backwards. But that mistake of mine was a localized brain fart: my overall point will still make sense, in fact more sense, if I fix this. So I'll go back and fix it.

But all this stuff was explaining a _guess_ of mine - the guess could be wrong. When we get around to actually composing some (enriched) profunctors, let's come back to this. We can try to see if we can express composition using left or right adjoints, like left or right (enriched) Kan extensions.

> If so I think you mean "the *right* adjoint to \\( \Delta : \mathbf{Set} \to \mathbf{Set}^2 \\) is the product \\( \times : \mathbf{Set}^2 \to \mathbf{Set} \\)".

Yes, I wrote those backwards. But that mistake of mine was a localized brain fart: my overall point will still make sense, in fact more sense, if I fix this. So I'll go back and fix it.

But all this stuff was explaining a _guess_ of mine - the guess could be wrong. When we get around to actually composing some (enriched) profunctors, let's come back to this. We can try to see if we can express composition using left or right adjoints, like left or right (enriched) Kan extensions.