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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