## 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.

Read more about Initial Algebra.

### 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

... If the category of F-

*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 ...### Famous quotes containing the words algebra and/or initial:

“Poetry has become the higher *algebra* of metaphors.”

—José Ortega Y Gasset (1883–1955)

“Capital is a result of labor, and is used by labor to assist it in further production. Labor is the active and *initial* force, and labor is therefore the employer of capital.”

—Henry George (1839–1897)

Main Site Subjects

Related Phrases

Related Words