Categories and Sheaves

By 柏原正樹, P. Schapira. 2005

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Derived equivalence for quantum symplectic resolutions (2011, background): “13 of [40]).”
Higher Segal Spaces (2012, neutral): “We recall the following standard result ([KS06a]).”
Hochschild homology and semiorthogonal decompositions (2009, background): “ quasicoherent sheaves on an algebraic variety is well known to be enhanced. The standard enhancement for it is provided by the DG-category of h-injective complexes of quasicoherent sheaves (see e.g. [KSch], Theorem 14.3.1). Starting from this enhancement one can produce many others. The most conven”
Categorical resolutions of irrational singularities (2012, neutral): “(2) This follows from (1) and [13].”
Derived equivalences from mutations of quivers with potential (2009, background): “ved category of A by Dpc(A) = D(Pcm(A)). Notice that the opposite category Dpc(A)op is isomorphic to D(Pcm(A)op) and that Pcm(A)op is a locally ﬁnite Grothendieck category. As shown in [17], cf. also [26], the category of complexes over a Grothendieck category admits a structure of Quillen model cat”
Lie groupoids and their orbispaces (2012, positive): “[16, § 7.1]).”