2019/03/19 by Louis Carlier, Carlier, Louis · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1903.07964
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.