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1. TODO: section 4 of the paper, and examples.

mattecapu

2. Change name to singular form (+ redirect for the plural form) to stick to the convention. See also the analogous change on the structured cospan page.

mattecapu

3. Typo in decoration definition

Micah Halter

• CommentRowNumber4.
• CommentAuthorSam Staton
• CommentTimeJun 30th 2020

I think there’s no less generality from taking $D=\mathbf{Set}$. If no-one objects, I suggest to replace $D$ with $\mathbf{Set}$ and then put a remark about this at the end of the article. The point is that the definition remains the same if you compose $F:C\to D$ with the global sections functor $D(I,-):D \to \mathbf{Set}$, which is monoidal.