Contents tagged with Functors
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Category Theory via C# (4) Natural Transformation
If F: C → D and G: C → D are both functors from categories C to category D, the mapping from F to G is called natural transformation and denoted α: F ⇒ G. α: F ⇒ G is actually family of morphisms from F to G, For each object X in category C, there is a specific morphism αX: F(X) → G(X) in category D, called the component of α at X. For each morphism m: X → Y in category C and 2 functors F: C → D, G: C → D, there is a naturality square in D:
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Category Theory via C# (3) Functor and LINQ to Functors
In category theory, functor is a mapping from category to category. Giving category C and D, functor F from category C to D is a structure-preserving morphism from C to D, denoted F: C → D: