In functional programming and category theory, a functor is a mapping between categories that preserves the structure of categories, such as objects and morphisms. It allows the application of functions over wrapped values, enabling the composition of operations while maintaining the context of the data structure.

Functor

Functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions and avoids changing state or mutable data. It emphasizes the use of pure functions, higher-order functions, and immutable data structures to promote code that is predictable, easier to test, and inherently parallelizable.

functional programming

Category Theory is a branch of mathematics that deals with abstract structures and relationships between them, providing a unifying framework to understand different mathematical concepts. It focuses on the composition of morphisms and the properties of objects, allowing for a high-level perspective that can reveal deep insights across various fields of mathematics and computer science.

category theory

functor

mapping between categories

structure of categories

Objects are fundamental elements in both physical and digital realms, serving as entities that encapsulate data and behavior, or physical properties. They play a crucial role in object-oriented programming and help in organizing code around real-world concepts, making it easier to manage and understand complex systems.

objects

Morphisms are structure-preserving mappings between mathematical objects, serving as the fundamental building blocks in category theory to study relationships between these objects. They generalize functions and homomorphisms, allowing for a unified treatment of various mathematical structures across different domains.

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