Category Theory via C# (8) Advanced LINQ to Monads https://weblogs.asp.net:443/dixin/category-theory-via-csharp-8-more-linq-to-monads [FP & LINQ via C# series][Category Theory via C# series]Monad is a powerful structure, with the LINQ support in C# language, monad enables chaining operations to build fluent workflow, which can be pure. With these features, monad can be used to manage I/O, state changes, exception handling, sSat, 31 Dec 2022 13:13:00 GMThttps://weblogs.asp.net:443/dixin/category-theory-via-csharp-8-more-linq-to-monadsC#.NETFunctional ProgrammingLINQCategory TheoryLINQ via C#MonadsCategory Theory via C# (7) Monad and LINQ to Monads https://weblogs.asp.net:443/dixin/category-theory-via-csharp-7-monad-and-linq-to-monads [FP & LINQ via C# series][Category Theory via C# series]MonadAs fore mentioned endofunctor category can be monoidal (the entire category. Actually, an endofunctor In the endofunctor category can be monoidal too. This kind of endofunctor is called monad. Monad is another important algebraicMon, 26 Dec 2022 13:13:00 GMThttps://weblogs.asp.net:443/dixin/category-theory-via-csharp-7-monad-and-linq-to-monadsC#.NETFunctional ProgrammingLINQCategory TheoryLINQ via C#MonadsCategory Theory via C# (6) Monoidal Functor and Applicative Functor https://weblogs.asp.net:443/dixin/category-theory-via-csharp-6-monoidal-functor-and-applicative-functor [FP & LINQ via C# series][Category Theory via C# series]Monoidal functorGiven monoidal categories (C, ⊗, IC) and (D, ⊛, ID), a strong lax monoidal functor is a functor F: C → D equipped with:Monoid binary multiplication operation, which is a natural transformation φ: F(Sun, 25 Dec 2022 13:12:00 GMThttps://weblogs.asp.net:443/dixin/category-theory-via-csharp-6-monoidal-functor-and-applicative-functorC#.NETFunctional ProgrammingLINQCategory TheoryLINQ via C#Applicative FunctorsMonadal FunctorsCategory Theory via C# (5) Bifunctor https://weblogs.asp.net:443/dixin/category-theory-via-csharp-5-bifunctor [FP & LINQ via C# series][Category Theory via C# series]BifunctorA functor is the mapping from 1 object to another object, with a “Select” ability to map 1 morphism to another morphism. A bifunctor (binary functor), as the name implies, is the mapping from 2 objects and from 2 morphisms. GiviThu, 15 Dec 2022 13:11:00 GMThttps://weblogs.asp.net:443/dixin/category-theory-via-csharp-5-bifunctorC#.NETFunctional ProgrammingLINQCategory TheoryCategoriesLINQ via C#BifunctorsMonadal CategoriesCategory Theory via C# (4) Natural Transformation https://weblogs.asp.net:443/dixin/category-theory-via-csharp-4-natural-transformation [FP & LINQ via C# series][Category Theory via C# series]Natural transformation and naturalityIf 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 iWed, 14 Dec 2022 13:10:00 GMThttps://weblogs.asp.net:443/dixin/category-theory-via-csharp-4-natural-transformationLINQ via C#C#.NETFunctional ProgrammingLINQCategory TheoryFunctorsNatural TransformationCategoriesCategory Theory via C# (3) Functor and LINQ to Functors https://weblogs.asp.net:443/dixin/category-theory-via-csharp-3-functor-and-linq-to-functors [FP & LINQ via C# series][Category Theory via C# series]Functor and functor lawsIn 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:F maps objTue, 13 Dec 2022 13:10:00 GMThttps://weblogs.asp.net:443/dixin/category-theory-via-csharp-3-functor-and-linq-to-functorsLINQ via C#C#.NETFunctional ProgrammingLINQCategory TheoryFunctorsCategory Theory via C# (2) Monoid https://weblogs.asp.net:443/dixin/category-theory-via-csharp-2-monoid [FP & LINQ via C# series][Category Theory via C# series]Monoid and monoid lawsMonoid is an important algebraic structure in category theory. A monoid M is a set M equipped with a binary operation ⊙ and a special element I, denoted 3-tuple (M, ⊙, I), whereM is a set of elements⊙ is a binaryMon, 12 Dec 2022 13:09:00 GMThttps://weblogs.asp.net:443/dixin/category-theory-via-csharp-2-monoidC#.NETFunctional ProgrammingLINQCategory TheoryCategoriesLINQ via C#Monoid`