Item 2 (018P) — The Clowder Project

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`

Componentwise Inverses of Natural Transformations Assemble Into Natural Transformations. Let $\alpha ^{-1}\colon G\Longrightarrow F$ be a transformation such that, for each $A\in \text{Obj}\webleft (\mathcal{C}\webright )$, we have
\begin{align*} \alpha ^{-1}_{A}\circ \alpha _{A} & = \text{id}_{F\webleft (A\webright )},\\ \alpha _{A}\circ \alpha ^{-1}_{A} & = \text{id}_{G\webleft (A\webright )}. \end{align*}

Then $\alpha ^{-1}$ is a natural transformation.

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