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A tree is a connected graph without cycles, with a finite or infinite number of vertices. There are many variants of trees, according to further constraints or decorations.

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What is the precise relationship between "prodsimplicial sets" and rooted trees?

X : \mathrm{Prism} \vdash C X : \mathrm{Prism} $ $ l : \mathrm{list}\ \mathrm{Prism} \vdash \Pi l : \mathrm{Prism} $ There are a short list of operations needed to generate the family of rooted trees … But if that worries you, you can argue that the strange plurality of trees is isomorphic to the strange plurality of products in a natural way. And that should be enough. …
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