Abstract
We define graphical properads as the free properads generated by connected wheel-free graphs. We observe that a graphical properad has an infinite set of elements precisely when the generating graph is not simply connected. The discussion of the tensor product of free properads in Chap. 4 applies in particular to graphical properads. Then we illustrate with several examples that a general properad map between graphical properads may exhibit bad behavior that would never happen when working with simply connected graphs. These examples serve as the motivation of the restriction on the morphisms in the graphical category.
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References
I. Moerdijk, B. Toën, Simplicial Methods for Operads and Algebraic Geometry. Advanced Courses in Mathematics, CRM Barcelona (Springer, Basel, 2010)
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© 2015 Springer International Publishing Switzerland
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Hackney, P., Robertson, M., Yau, D. (2015). Graphical Properads. In: Infinity Properads and Infinity Wheeled Properads. Lecture Notes in Mathematics, vol 2147. Springer, Cham. https://doi.org/10.1007/978-3-319-20547-2_5
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DOI: https://doi.org/10.1007/978-3-319-20547-2_5
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-20546-5
Online ISBN: 978-3-319-20547-2
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