Wendy Lowen

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In this paper we develop the basic infinitesimal deformation theory of abelian categories. This theory yields a natural generalization of the wellknown deformation theory of algebras developed by Gerstenhaber. As part of our deformation theory we define a notion of flatness for abelian categories. We show that various basic properties are preserved under(More)
It is a general philosophy that the Hochschild complex of a mathematical object governs its deformation theory and that, in particular, the second Hochschild cohomology group parametrizes its first-order deformations. This, of course, holds true for associative algebras [3], and more generally for schemes and abelian categories ([9], see also [1]). From the(More)
For a ringed space (X,O), we show that the deformations of the abelian category Mod(O) of sheaves of O-modules [11] are obtained from algebroid prestacks, as introduced by Kontsevich. In case X is a quasi-compact separated scheme the same is true for Qch(O), the category of quasi-coherent sheaves on X. It follows in particular that there is a deformation(More)
We generalize and clarify Gerstenhaber and Schack’s “Special Cohomology Comparison Theorem”. More specifically we obtain a fully faithful functor between the derived categories of bimodules over a prestack over a small category U and the derived category of bimodules over its corresponding fibered category. In contrast to Gerstenhaber and Schack we do not(More)
Functional topology is concerned with developing topological concepts in a category endowed with certain axiomatically defined classes of morphisms (Clementino et al. 2004). In this paper, we extend functional topology to a monoidal framework, replacing categorical pullbacks by pullbacks relative to the monoidal structure (which itself replaces the product)(More)