Geodesic
Closed dendroidal sets and unital operads
Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 118-170.

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We discuss a variant of the category of dendroidal sets, the so-called closed dendroidal sets which are indexed by trees without leaves. This category carries a Quillen model structure which behaves better than the one on general dendroidal sets, mainly because it satisfies the pushout-product property, hence induces a symmetric monoidal structure on its homotopy category. We also study complete Segal style model structures on closed dendroidal spaces, and various Quillen adjunctions to model categories on (all) dendroidal sets or spaces. As a consequence, we deduce a Quillen equivalence from closed dendroidal sets to the category of unital simplicial operads, as well as to that of simplicial operads which are unital up-to-homotopy. The proofs exhibit several new combinatorial features of categories of closed trees.
Publié le :
Classification : 18M75, 18N70, 18N40
Keywords: unital operad, dendroidal set, dendroidal space, Quillen equivalence 
@article{TAC_2021_36_a4,
     author = {Ieke Moerdijk},
     title = {Closed dendroidal sets and unital operads},
     journal = {Theory and applications of categories},
     pages = {118--170},
     publisher = {mathdoc},
     volume = {36},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2021_36_a4/}
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Ieke Moerdijk. Closed dendroidal sets and unital operads. Theory and applications of categories, The Rosebrugh Festschrift, Tome 36 (2021), pp. 118-170. http://geodesic.mathdoc.fr/item/TAC_2021_36_a4/