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2010 The homotopy theory of strong homotopy algebras and bialgebras
J. P. Pridham
Homology Homotopy Appl. 12(2): 39-108 (2010).


Lada introduced strong homotopy algebras to describe the structures on a deformation retract of an algebra in topological spaces. However, there is no satisfactory general definition of a morphism of strong homotopy (s.h.) algebras. Given a monad $\top$ on a simplicial category $\mathcal{C}$, we instead show how s.h. $\top$-algebras over $\mathcal{C}$ naturally form a Segal space. Given a distributive monad-comonad pair ($\top, \bot$), the same is true for s.h. ($\top, \bot$)-bialgebras over $\mathcal{C}$; in particular this yields the homotopy theory of s.h. sheaves of s.h. rings. There are similar statements for quasi-monads and quasi-comonads. We also show how the structures arising are related to derived connections on bundles.


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J. P. Pridham. "The homotopy theory of strong homotopy algebras and bialgebras." Homology Homotopy Appl. 12 (2) 39 - 108, 2010.


Published: 2010
First available in Project Euclid: 28 January 2011

zbMATH: 1236.18016
MathSciNet: MR2721031

Primary: 18C15 , 18D20 , 18G30 , 55U40

Keywords: Algebraic theories , Segal spaces , simplicial categories

Rights: Copyright © 2010 International Press of Boston


Vol.12 • No. 2 • 2010
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