A simplicial category of homotopy gebras over properads is constructed, and infinity-quasi-isomorphisms are shown to coincide with zig-zags of quasi-isomorphisms.
The higher algebra of topological recursion
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Simplicial properadic homotopy
A simplicial category of homotopy gebras over properads is constructed, and infinity-quasi-isomorphisms are shown to coincide with zig-zags of quasi-isomorphisms.