Category theory starts with the observation that many properties of mathematical systems can be unified and simplified by a presentation with diagrams of arrows. Each arrow f : X → Y represents a function; that is, a set X, a set Y, and a rule x ↦ f x which assigns to each element x ∈ X an element f x ∈ Y; whenever possible we write f x and not f(x), omitting unnecessary parentheses.
KeywordsAbelian Group Topological Space Diagram Commute Category Theory Universal Property
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