exploring Universal Constructions

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void = initial object = in SET Category, empty set = in logic, proving “false”

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initial object = for every point in a category there is one and only one arrow from the initial object to the point

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identity exists, void -> void

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nothing can return void

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anything that takes in a void can return any type, void -> a

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unit = terminal object = () = in SET Category, set with one element = in logic, proving “true”

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terminal object = from every point in a category, there is one and only one arrow to the terminal object

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two terminal objects are always have a uniquely ismorphic = only one way to isomorph between the two

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you can return a unit from anything, a -> ()

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can use unit to define the element of a set, one :: () -> int, two :: () -> int

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as many unit -> t functions exist as elements in the type t

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instead of talking about elements in category theory, we can talk about the function from unit

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bool = in SET Category, set with two elements

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Ideas from [[Category Theory]]