Tannakian Reconstruction in a Yoneda Equipment

The reason I bored you with the Yoneda equipment was to eventually double back to Tannakian reconstruction. In a nutshell, Tannakian reconstruction lets us reconstruct the hom-set from a set of natural transformations between fiber functors: Here, the end goes over the presheaf category. We have previously learned that we can define a presheaf object