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1. Function Composition

   Linked via "vector spaces"

   Category Theory
   In category theory, function composition is formalized as the primary associative binary operation on the morphisms within a category. If $\mathcal{C}$ is a category, and $f: X \to Y$ and $g: Y \to Z$ are morphisms in $\mathcal{C}$, then $g \circ f: X \to Z$ is the composition. This framework generalizes the concept beyond sets and functions to abstract structures like topological spaces,…

2. Jordan Algebras

   Linked via "vector space"

   Definition and Axiomatics
   A Jordan algebra $J$ over a field $F$ (often $\mathbb{R}$ or $\mathbb{C}$, though investigations over fields with characteristic 3 have shown surprising resilience) is a vector space equipped with a binary product, denoted by $\circ$, that satisfies two key axioms:
   Commutativity: For all $x, y \in J$:

3. Jordan Algebras

   Linked via "vector space"

   Classification and Exceptional Algebras
   Jordan algebras are classified based on the dimension of the underlying vector space and whether they are special.
   Albert Algebras