The author defines categories of normed bimodules over quiver tensor rings and claims an initial object whose unique morphisms give integrals, Taylor series, and Fourier series; the power-series claim rests on a false density statement.
Normed modules, integral sequences, and integrals with variable upper limits
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abstract
This paper provides a new categorification of the Lebesgue integral with variable upper limits by using normed modules over finite-dimensional $\Bbbk$-algebras $\mathit{\Lambda}$ and the category $\mathscr{A}^p_{\mathit{\Lambda}}$ associated with $\mathit{\Lambda}$. The integration process is redefined through the introduction of an integral partially ordered set and an abstract integral with variable upper limits. Finally, we present two important applications: (1) the categorification of basic elementary functions, including (anti-)trigonometric and logarithmic functions, and (2) a new approach for characterizing the global dimensions of gentle algebras.
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Normed representations of weight quivers
The author defines categories of normed bimodules over quiver tensor rings and claims an initial object whose unique morphisms give integrals, Taylor series, and Fourier series; the power-series claim rests on a false density statement.