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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
Representation theory of some infinite-dimensional algebras arising in continuously controlled algebra and topology
In this paper we determine the representation type of some algebras of
infinite matrices continuously controlled at infinity by a compact metrizable
space. We explicitly classify their finitely presented modules in the finite
and tame cases. The algebra of row-column-finite (or locally finite) matrices
over an arbitrary field is one of the algebras considered in this paper, its
representation type is shown to be finite.Comment: 33 page
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