Proposition. Natural transformations pair of adjunctions [31KN]

Let L,L′L, L' be two left adjoints, and their right adjoints are R,R′R, R' respectively, a natural transformation α:L→L′\alpha : L \to L' has a correspondence β:R′→R\beta : R' \to R.

Proof [local-0]

We can construct

figure tex6800