Products in the category of 𝕑2n-manifolds

DOI

10.1080/14029251.2019.1613051How to use a DOI?

Keywords

𝕑2n-geometry; finite categorical product; product morphism; sheafification; locally convex topological algebra; completed tensor product

Abstract

We prove that the category of 𝕑2n-manifolds has all finite products. Further, we show that a 𝕑2n-manifold (resp., a 𝕑2n-morphism) can be reconstructed from its algebra of global 𝕑2n-functions (resp., from its algebra morphism between global 𝕑2n-function algebras). These results are of importance in the study of 𝕑2n Lie groups. The investigation is all the more challenging, since the completed tensor product of the structure sheafs of two 𝕑2n-manifolds is not a sheaf. We rely on a number of results on (pre)sheaves of topological algebras, which we establish in the appendix.

Copyright

© 2019 The Authors. Published by Atlantis and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Andrew Bruce
AU  - Norbert Poncin
PY  - 2021
DA  - 2021/01/06
TI  - Products in the category of 𝕑2n-manifolds
JO  - Journal of Nonlinear Mathematical Physics
SP  - 420
EP  - 453
VL  - 26
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2019.1613051
DO  - 10.1080/14029251.2019.1613051
ID  - Bruce2021
ER  -