Coalgebra

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Let [math]\mathbf{C}[/math] be a category and [math]F : \mathbf{C} \to \mathbf{C}[/math] an endofunctor on [math]\mathbf{C}[/math]. An [math]F[/math]-coalgebra is a morphism [math]c : X \to F X[/math] in [math]\mathbf{C}[/math].