The paper extends Dold-Kan theory to categories of finite relational structures, classifies their irreducible representations, and proves a monoidal generalization of Artin's reconstruction theorem equating uniformly continuous representations of transformation monoids with sheaves on those category
Uniformly Presented Vector Spaces
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abstract
Gaussian elimination answers any question about a finitely presented vector space. However, a "uniform family" of such presentations--given as generic relations among an unspecified number of generators--is susceptible to elimination only once the number of generators is fixed. We develop a theory of "uniformly presented vector spaces" to compute with these uniform families, introducing a formalism of finitely generated functors from the category of finite sets to the category of finite dimensional Q-vector spaces. We show that these representations have finite length and polynomial dimension away from the empty set, and produce finite leftward resolutions by manageable functors.
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2026 1verdicts
UNVERDICTED 1representative citing papers
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Representations of categories of finite relational structures and associated endomorphism monoids
The paper extends Dold-Kan theory to categories of finite relational structures, classifies their irreducible representations, and proves a monoidal generalization of Artin's reconstruction theorem equating uniformly continuous representations of transformation monoids with sheaves on those category