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  1. Function Composition

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    Category Theory
    In category theory, function composition is formalized as the primary associative binary operation on the morphisms within a category. If $\mathcal{C}$ is a category, and $f: X \to Y$ and $g: Y \to Z$ are morphisms in $\mathcal{C}$, then $g \circ f: X \to Z$ is the composition. This framework generalizes the concept beyond sets and functions to abstract structures like topological spaces,…