Adjointness of Derived Direct and Inverse Image

Proposition 3.2.1. For any ringed-space map f X Y, there is a natural hifunctorial isomorphism, 

There is a simple equivalence between giving the adjunction isomorphism (3.2.1) and giving functorial morphisms 

Define e to be the unique A-functorial map such that the following natural diagram in D(X) commutes for all B G K(X)  

To see then that the first row in (3.2.1.1) is the identity, i.e., that its composition with the canonical map C- f R/ is just itself, consider the 

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Adjointness of Derived Direct and Inverse Image corresponds via (2.6.1) to the composed map... 

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