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arXiv · 2404.08139

Towards a General Theory of Dependent Sums

Peter Bonart
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Abstract

We introduce dependent adders. A dependent adder $A$ has for every $x \in A$ a way of adding together $x$ many elements of $A$. We provide examples from many disparate branches of mathematics. Examples include the field with one element $\mathbb{F}_1$, the real numbers with integrals as sums, the category of categories with oplax colimits as sums. We also consider modules over dependent adders and provide examples.

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Peter Bonart. 2024-04-11. Towards a General Theory of Dependent Sums. https://arxiv.org/abs/2404.08139

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