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- Wendy Lowen, Anne Smythe
- The Medical journal of Australia
- 1962

- Wendy Lowen
- 2008

In this paper we develop the obstruction theory for lifting complexes, up to quasi-isomorphism, to derived categories of flat nilpotent deformations of abelian categories. As a particular case we also obtain the corresponding obstruction theory for lifting of objects in terms of Yoneda Extgroups. In appendix we prove the existence of miniversal derived… (More)

- Wendy Lowen
- 2008

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)

- Wendy Lowen
- 2008

A notion of Hochschild cohomology HH∗(A) of an abelian category A was defined by Lowen and Van den Bergh (2005) and they showed the existence of a characteristic morphism χ from the Hochschild cohomology of A into the graded centre Z∗(Db(A)) of the bounded derived category of A. An element c ∈ HH2(A) corresponds to a first order deformation Ac of A (Lowen… (More)

- Bernhard Keller, Wendy Lowen, Dmitry Kaledin, Wendy Lowen
- 2009

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)

- Wendy Lowen
- 2008

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)

- Wendy Lowen
- 2009

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)

- Wendy Lowen, Joris Mestdagh
- Applied Categorical Structures
- 2016

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)

- Wendy Lowen
- 2008

For a scheme X, we construct a sheaf C of complexes on X such that for every quasi-compact open U ⊂ X, C(U) is quasi-isomorphic to the Hochschild complex of U [11]. Since C is moreover acyclic for taking sections on quasi-compact opens, we obtain a local to global spectral sequence for Hochschild cohomology if X is quasi-compact.

- Wendy Lowen
- Australasian radiology
- 1973