Item 1 (00XT) — The Clowder Project

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Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
Style 4	`book`	Computer Modern	`amsthm`

*To be replaced with Linus Romer's Elemaints when it is released.

The precomposition function associated to $f$ is the function
\[ f^{*} \colon \textup{Hom}_{\mathcal{C}}\webleft (B,C\webright ) \to \textup{Hom}_{\mathcal{C}}\webleft (A,C\webright ) \]

defined by

\[ f^{*}\webleft (\phi \webright ) \mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\phi \circ f \]

for each $\phi \in \textup{Hom}_{\mathcal{C}}\webleft (B,C\webright )$.

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