TY - JOUR
T1 - ∞-Operads as Analytic Monads
AU - Gepner, David
AU - Haugseng, Rune
AU - Kock, Joachim
N1 - Funding Information:
This work was supported by National Science Foundation [DMS-1406529 and DMS-1714273 to D.G.];
Publisher Copyright:
© 2021 The Author(s). Published by Oxford University Press. All rights reserved.
PY - 2022/8/1
Y1 - 2022/8/1
N2 - We develop an ∞ -categorical version of the classical theory of polynomial and analytic functors, initial algebras, and free monads. Using this machinery, we provide a new model for ∞ -operads, namely ∞ -operads as analytic monads. We justify this definition by proving that the ∞ -category of analytic monads is equivalent to that of dendroidal Segal spaces, known to be equivalent to the other existing models for ∞ -operads.
AB - We develop an ∞ -categorical version of the classical theory of polynomial and analytic functors, initial algebras, and free monads. Using this machinery, we provide a new model for ∞ -operads, namely ∞ -operads as analytic monads. We justify this definition by proving that the ∞ -category of analytic monads is equivalent to that of dendroidal Segal spaces, known to be equivalent to the other existing models for ∞ -operads.
UR - https://www.scopus.com/pages/publications/85136026853
U2 - 10.1093/imrn/rnaa332
DO - 10.1093/imrn/rnaa332
M3 - Article
AN - SCOPUS:85136026853
SN - 1073-7928
VL - 2022
SP - 12516
EP - 12624
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 16
ER -