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Dendroidal Sets and Simplicial Operads
, 2011
"... We establish a Quillen equivalence relating the homotopy theory of Segal operads and the homotopy theory of simplicial operads, from which we deduce that the homotopy coherent nerve functor is a right Quillen equivalence ..."
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We establish a Quillen equivalence relating the homotopy theory of Segal operads and the homotopy theory of simplicial operads, from which we deduce that the homotopy coherent nerve functor is a right Quillen equivalence
Free Products of Higher Operad Algebras
, 909
"... Abstract. One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2categories. In this paper we continue the developments of [3] and [2] by understanding the natural generalisations of Gray’s little brother, ..."
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Abstract. One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2categories. In this paper we continue the developments of [3] and [2] by understanding the natural generalisations of Gray’s little brother, the funny tensor product of categories. In fact we exhibit for any higher categorical structure definable by an noperad in the sense of Batanin [1], an analogous tensor product which forms a symmetric monoidal closed structure
A Model Structure for Enriched Coloured Operads
"... Abstract. We prove that, under certain conditions, the model structure on a monoidal model category V can be transferred to a model structure on the category of Venriched coloured (symmetric) operads. As a particular case we recover the known model structure on simplicial operads. ..."
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Abstract. We prove that, under certain conditions, the model structure on a monoidal model category V can be transferred to a model structure on the category of Venriched coloured (symmetric) operads. As a particular case we recover the known model structure on simplicial operads.
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, 903
"... Abstract. In this article, we further the study of higher Ktheory of dg categories via universal invariants, initiated in [33]. Our main result is the corepresentability of nonconnective Ktheory by the base ring in the universal localizing motivator. As an application, we obtain for free higher C ..."
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Abstract. In this article, we further the study of higher Ktheory of dg categories via universal invariants, initiated in [33]. Our main result is the corepresentability of nonconnective Ktheory by the base ring in the universal localizing motivator. As an application, we obtain for free higher Chern characters, resp. higher trace maps, from negative Ktheory to cyclic homology,
Dendroidal Sets as Models for . . .
, 2009
"... The homotopy theory of ∞operads is defined by extending Joyal’s ..."