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2023•arXiv (Cornell University)Open access

A short note on coproducts of abelian pro-Lie groups

Wolfgang Herfort, Karl H. Hofmann, Francesco G. Russo

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Abstract

The notion of conditional coproduct of a family of abelian pro-Lie groups in the category of abelian pro-Lie groups is introduced. It is shown that the cartesian product of an arbitrary family of abelian pro-Lie groups can be characterized by the universal property of the conditional coproduct.

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The notion of conditional coproduct of a family of abelian pro-Lie groups in the category of abelian pro-Lie groups is introduced. It is shown that the cartesian product of an arbitrary family of abelian pro-Lie groups can be characterized by the universal property of the conditional coproduct.

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Available abstract

The notion of conditional coproduct of a family of abelian pro-Lie groups in the category of abelian pro-Lie groups is introduced. It is shown that the cartesian product of an arbitrary family of abelian pro-Lie groups can be characterized by the universal property of the conditional coproduct.

Key concepts: Coproduct, Abelian group, Mathematics, Pure mathematics, Elementary abelian group, Lie group, Cartesian product, Product (mathematics)

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