Item 1 (01UZ) — 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`
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*To be replaced with Linus Romer's Elemaints when it is released.

Proof of Item (a): We may partition the monoidality diagram for $\text{id}^{\otimes }$ of Item 2 of Remark 10.1.1.1.3 as follows:

Since:
- Subdiagram (1) commutes by Item (a) of Item 1.
- Subdiagram (2) commutes by assumption.
- Subdiagram (3) commutes by assumption.
it follows that the boundary diagram also commutes, i.e. $\text{id}^{\otimes }$ satisfies the monoidality condition of Item 2 of Remark 10.1.1.1.3.

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