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On an Enhancement of the Category of Shifted L<inf>∞</inf>-Algebras
Dolgushev, VA Rogers, CL
Dolgushev, VA
Rogers, CL
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2017-08-01
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10.1007/s10485-016-9424-4
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© 2016, Springer Science+Business Media Dordrecht. We construct a symmetric monoidal category SLie∞MC whose objects are shifted L∞-algebras equipped with a complete descending filtration. Morphisms of this category are “enhanced” infinity morphisms between shifted L∞-algebras. We prove that any category enriched over SLie∞MC can be integrated to a simplicial category whose mapping spaces are Kan complexes. The advantage gained by using enhanced morphisms is that we can see much more of the simplicial world from the L∞-algebra point of view. We use this construction in a subsequent paper (Dolgushev et al. Adv. Math. 274, 562–605, 2015) to produce a simplicial model of a (∞,1)-category whose objects are homotopy algebras of a fixed type.
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Springer Science and Business Media LLC
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Applied Categorical Structures
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