What is initial algebra?

Initial Algebra

In mathematics, an initial algebra is an initial object in the category of F-algebras for a given endofunctor F. The initiality provides a general framework for induction and recursion.

Some articles on initial algebra:

Initial Algebra - Use in Computer Science
... data structures used in programming, such as lists and trees, can be obtained as initial algebras of specific endofunctors ... While there may be several initial algebras for a given endofunctor, they are unique up to isomorphism, which informally means that the "observable" properties of a data structure can be ... that the list-forming operations are Combined into one function, they give , which makes this an F-algebra for the endofunctor F sending to ...
Initial F-algebra
... If the category of F-algebras for a given endofunctor F has an initial object, it is called an initial algebra ... The algebra in the above example is an initial algebra ... structures used in programming, such as lists and trees, can be obtained as initial algebras of specific endofunctors ...

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