Infinity Properads and Infinity Wheeled Properads by Philip Hackney Marcy Robertson & Donald Yau

Author:Philip Hackney, Marcy Robertson & Donald Yau
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

This is true because the free properad is obtained from its underlying operad, which is the free operad generated by T, by adding empty components.

There are similar full subcategories of Γ defined by the indicated subsets of graphs: , where Gr di ↑ is the set of simply connected graphs,

, where Gr ci ↑ is the set of connected wheel-free graphs with non-empty inputs, and

, where Gr co ↑ is the set of connected wheel-free graphs with non-empty outputs.

Using the above isomorphism and equivalence of categories, there is a commutative diagram of subcategory inclusions:

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