Lemma 63.6.3. Let f : X \to Y and g : Y \to Z be separated and locally quasi-finite morphisms. There is a canonical isomorphism (g \circ f)^! \to f^! \circ g^!. Given a third locally quasi-finite morphism h : Z \to T the diagram
\xymatrix{ (h \circ g \circ f)^! \ar[r] \ar[d] & f^! \circ (h \circ g)^! \ar[d] \\ (g \circ f)^! \circ h^! \ar[r] & f^! \circ g^! \circ h^! }
commutes.
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