Isbell conjugacy

Dear All, I hope and pray you and your families are all well. If I may, Isbell conjugacy (https://conceptualmathematics.wordpress.com/2022/08/30/birkhoffs-theorem-fro...; see p. 17 in http://tac.mta.ca/tac/reprints/articles/8/tr8.pdf; given the current world situation, I thought it is good to have a copy of important papers in multiple locations) is about a category of contravariant functors and the dual category of a category of covariant functors. Is Isbell conjugacy implicit in CO- and CONTRA-VARIANCE and DUALIZATION? Pardon me if this is silly. I eagerly look forward to your corrections and clarifications. Happy Daughters' Day :-) Thanking you, posina [For admin and other information see: http://www.mta.ca/~cat-dist/ ]