> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/450-category-theory/10-morphisms/catamorphism.md).

# Catamorphism

<https://en.wikipedia.org/wiki/Catamorphism>

The concept of catamorphism (Greek: κατά "downwards") denotes the unique homomorphism from an *initial algebra* into some other algebra.

In FP, catamorphisms provide *generalizations of folds of lists* to arbitrary algebraic data types, which can be described as initial algebras. The dual concept is that of *anamorphism that generalize unfolds*.