In mathematics, specifically in category theory, an <math>F</math>-algebra for an endofunctor <math>F : \mathcal{C}\longrightarrow \mathcal{C}</math> is an object <math>A</math> of <math>\mathcal{C}</math> together with a <math>\mathcal{C}</math>-morphism <math>\alpha : FA \longrightarrow A</math>. In this sense F-algebras are dual to F-coalgebras.
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- In mathematics, specifically in category theory, an <math>F</math>-algebra for an endofunctor <math>F : \mathcal{C}\longrightarrow \mathcal{C}</math> is an object <math>A</math> of <math>\mathcal{C}</math> together with a <math>\mathcal{C}</math>-morphism <math>\alpha : FA \longrightarrow A</math>. In this sense F-algebras are dual to F-coalgebras. A homomorphism from <math>F</math>-algebra <math>(A, \alpha)</math> to <math>F</math>-algebra <math>(B, \beta)</math> is a morphism <math>f:A\longrightarrow B</math> in <math>\mathcal{C}</math> such that <math> f\circ \alpha = \beta \circ Ff</math>. Thus the <math>F</math>-algebras constitute a category.
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- In mathematics, specifically in category theory, an <math>F</math>-algebra for an endofunctor <math>F : \mathcal{C}\longrightarrow \mathcal{C}</math> is an object <math>A</math> of <math>\mathcal{C}</math> together with a <math>\mathcal{C}</math>-morphism <math>\alpha : FA \longrightarrow A</math>. In this sense F-algebras are dual to F-coalgebras.
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