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Abstract
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We exhibit the simplex category
and Segal’s category
as
–categorical localizations of
the dendroidal categories
and
introduced by Moerdijk and Weiss. As an application we obtain an equivalence of
–categories between
invertible
–operads
and the
–Segal
spaces of Dyckerhoff and Kapranov. Finally, we describe a
cyclic version of the dendroidal category and explain how it
–localizes to Connes’
cyclic category
.
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Keywords
simplicial objects, $2$–Segal spaces, infinity-operads,
dendroidal objects
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Mathematical Subject Classification 2010
Primary: 18D50, 18G30
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Publication
Received: 18 June 2019
Revised: 17 January 2020
Accepted: 29 January 2020
Published: 25 February 2021
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