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.
Comments (0)