Towards a General Theory of Dependent Sums
Abstract
We introduce dependent adders. A dependent adder A has for every x ∈ 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 F1, 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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.