@Anindya

I think you have a typo.

> > (1) \\(\qquad\Phi : \mathcal{X}^\text{op} \nrightarrow \mathcal{Y}\\) is a profunctor

should say

> > (1) \\(\qquad\Phi : \mathcal{X} \nrightarrow \mathcal{Y}\\) is a profunctor