Item 2 (01V0) — 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 (b): We may partition the monoidality diagram for $\text{id}^{\otimes }$ of Item 2 of Remark 10.1.1.1.3 as follows:

Since:
- Subdiagram $\webleft (1\webright )$ commutes by assumption.
- Subdiagram $\webleft (2\webright )$ commutes by assumption.
- Subdiagram $\webleft (3\webright )$ commutes by Item (b) of Item 1.
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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