What do dg-categories form?

By D. Tamarkin. Compositio Mathematica, 2006

53 citations recorded by the source corpus.

We introduce a homotopy 2-category structure on the collection of dg-categories, dg-functors, and their derived transformations. This construction provides for a conceptual proof of Deligne's conjecture on Hochschild cochains.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/822c57d15d56d52031529bd822869a0445515f4b

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Citations in the corpus

Hirzebruch–Riemann–Roch‐type formula for DG algebras (2007, background): “ototype is the pull-back functor associated with a morphism of schemes). The real deﬁnition is more subtle and we won’t discuss it here referring the reader to more thorough treatments of the subject [20, 35, 62, 63, 65, 66]. Here is an interesting question: Is it possible to tell whether a noncommu”
Symmetrisation of n-operads and compactification of real configuration spaces (2006, methodology): “In the particular case of a DG-category with one object and transformations of the identity functor, we obtain the Hochschild complex of an associative algebra and then we apply our Theorem 8.7 [ 23 ].”
Operadic categories and Duoidal Deligne's conjecture (2014, background): “contractible 2-operad in the sense of the ﬁrst author [3] on the homotopical center of a monoid [9, Corollary 11.20]. We call this statement duoidal Deligne’s conjecture. Tamarkin’s main theorem from [30] is a particular case of this conjecture. Classical Deligne’s conjecture also follows from the d”
Symmetries (2014, unknown): “This action should explain the proof of Deligne’s conjecture given by Tamarkin [11], in particular why there are 2 -discs acting on the Hochschild cohomology.”
Operadic Twisting -- with an application to Deligne's conjecture (2012, background): “d, we deduce Theorem 9.3 from [8, Lemma A.3]. 9.3. The dg operad Br is a homotopy xed point of Tw. Various solutions of the Deligne conjecture on Hochschild cochain complex [1], [2], [9], [26], [21], [30], [31] imply that the dg operad Br is quasi-isomorphic to the dg operad C (E 2;K) of singular c”
A DG Guide to Voevodsky’s Motives (2006, background): “9.2; Icdh tr 6.9.3; I∆ tr 2.3; ItrNis 4.4; INistr 4.3; IZar tr 2.3; K·M 6.8; M(X) 2.3; Mc(X) 6.9.4; o2.1.2; P, Ptr 2.1.4; PSh1.10, 2.1.1; PShtr 2.1.2; ShT 1.11, R, R-mod 1.1; R-dgm 1.6.3; 61 RM 2.3; R[T], R[U·], R[X/Y] 1.10; R(n) 2.2; R[G]-perm 2.4; Rtr, Rtr[X] 2.1.2; Rtr(n) 2.2; R∆ tr[X], R∆ tr(n) ”