Spaces of Operad Structures

Details Spaces of Operad Structures Spaces of Operad Structures

2011-11-16

arxiv.org/abs/1111.3904v1

Mathematics

Algebraic Topology

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Scientific paper

The purpose of this paper is to study the derived category of simplicial multicategories with arbitrary sets of objects (also known as, colored operads in simplicial sets). Our main result is a derived Morita theory for operads-where we describe the derived mapping spaces between two multicategories P and Q in terms of the nerve of a certain category of P-Q-bimodules. As an application, we show that the derived category possesses internal Hom-objects.

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