Lemma 6.21.6. Let f : X \to Y and g : Y \to Z be continuous maps of topological spaces. The functors (g \circ f)^{-1} and f^{-1} \circ g^{-1} are canonically isomorphic. Similarly (g \circ f)_ p \cong f_ p \circ g_ p on presheaves.
Proof. To see this use that adjoint functors are unique up to unique isomorphism, and Lemma 6.21.2. \square
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