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arXiv · 1903.07964

Hereditary species as monoidal decomposition spaces, comodule bialgebras, and operadic categories

Louis Carlier
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Abstract

We show that Schmitt's hereditary species induce monoidal decomposition spaces, and exhibit Schmitt's bialgebra construction as an instance of the general bialgebra construction on a monoidal decomposition space. We show furthermore that this bialgebra structure coacts on the underlying restriction-species bialgebra structure so as to form a comodule bialgebra. Finally, we show that hereditary species induce a new family of examples of operadic categories in the sense of Batanin and Markl.

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Louis Carlier. 2019-03-19. Hereditary species as monoidal decomposition spaces, comodule bialgebras, and operadic categories. https://arxiv.org/abs/1903.07964

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