Jan 1, 2025
fuck you *forgets your group is a group and only remembers it's a set now*
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fuck you *forgets your group is a group and only remembers it's a set now*
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is this how spanish mathematicians notate the direct image w compact support
💥Monoids in functional Programming💥
Why Monoids? 👉 Ensure failsafe combination using monoids
👉Monoids are useful because you can perform ‘safe’ operations with them
👉 A semigroup is not a fail-safe operation. Monoids can take as many values or none, an still returns something by default.
👉Semigroup has a 🙌 concat method👈
A semigroup is a type with a concat method. Semigroups Definition 👉 Semigroups : Semigroups come from abstract algebra and laws and properties that come with this mathematical structure. 👉 The property is called associativity. 👉 If we say 1 + 1 + 1 is the same as 1 + (1 + 1). It does not matter how we group the operations. It will always the same result. That is one property we get from semigroups. Associativity Law if we combine three strings by saying (r + s + t), the operation is associative—it doesn’t matter whether we parenthesize it: ((r + s) + t) or (r + (s + t)).
👉Functor Laws👈 for Functors (identity, Composable)
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🙌Lambda in Functional Programming🙌
Category Theory & Category Laws in Functional Programming
🙌Pointed Functor in functional programming 🙌
A pointed functor is really a functor F together with a function of defined for every type a, and sending a value x of type a into a value of(x) of type F a.
The function "of" must be a natural transformation from the identity functor into F. Which means that of applied to a function's value equals of applied to the function's argument and then mapped over the function.
You may have heard of functions such as pure, point, unit, and return. These are various monikers for our of method.