41,178 research outputs found
Modules as exact functors
We can define a module to be an exact functor on a small abelian category.
This is explained and shown to be equivalent to the usual definition but it
does offer a different perspective, inspired by the notions from model theory
of imaginary sort and interpretation. A number of examples are worked through
Multisorted modules and their model theory
Multisorted modules, equivalently representations of quivers, equivalently
additive functors on preadditive categories, encompass a wide variety of
additive structures. In addition, every module has a natural and useful
multisorted extension by imaginaries. The model theory of multisorted modules
works just as for the usual, 1-sorted modules. A number of examples are
presented, some in considerable detail
Ringel's conjecture for domestic string algebras
We classify indecomposable pure injective modules over domestic string
algebras, verifying Ringel's conjecture on the structure of such modules.Comment: minor correction
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