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Normed modules and the categorification of integrations, series expansions, and differentiations
- Publication Year :
- 2024
-
Abstract
- We explore the assignment of norms to $\Lambda$-modules over a finite-dimensional algebra $\Lambda$, resulting in the establishment of normed $\Lambda$-modules. Our primary contribution lies in constructing a new category $\mathscr{N}\!\!or^p$ related to normed modules along with its full subcategory $\mathscr{A}^p$. By examining the objects and morphisms in these categories, we establish a framework for understanding the categorification of integration, series expansions and derivatives. Furthermore, we obtain the Stone--Weierstrass approximation theorem in the sense of $\mathscr{A}^p$.<br />Comment: 36 pages, 1 figures
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2405.02777
- Document Type :
- Working Paper