Item 1 (01US) — The Clowder Project

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Style 1	`book`	Alegreya Sans	`tcbthm`
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*To be replaced with Linus Romer's Elemaints when it is released.

Extra Monoidality Conditions. Let $\big (\text{id}^{\otimes }_{\mathcal{C}},\text{id}^{\otimes }_{\mathbb {1}|\mathcal{C}}\big )$ be a morphism of $\mathcal{M}_{\mathbb {E}_{1}}\webleft (\mathcal{C}\webright )$ from $\webleft(\phantom{\mathrlap {\lambda ^{\mathcal{C}}}}\mathcal{C}\right.$, $\otimes _{\mathcal{C}}$, $\mathbb {1}_{\mathcal{C}}$, $\alpha ^{\mathcal{C}}$, $\lambda ^{\mathcal{C}}$, $\left.\rho ^{\mathcal{C}}\webright)$ to $\webleft(\phantom{\mathrlap {\lambda ^{\mathcal{C},\prime }}}\mathcal{C}\right.$, $\boxtimes _{\mathcal{C}}$, $\mathbb {1}'_{\mathcal{C}}$, $\alpha ^{\mathcal{C},\prime }$, $\lambda ^{\mathcal{C},\prime }$, $\left.\rho ^{\mathcal{C},\prime }\webright)$.
1. The diagram
  
  commutes.
2. The diagram
  
  commutes.

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