The Morphism Cube

Recursion Schemes in Category Theory

⦇⦈ Catamorphism

κατά (down) + μορφή (form)

μF → A

The fundamental fold operation. Consumes an inductive structure to produce a value. The unique F-algebra homomorphism from the initial algebra.

Fold / Consume structures

Fold (Catamorphism family)

Unfold (Anamorphism family)

Temporal extension

Spatial extension

Combined schemes

↑ Temporal

→ Spatial

↗ Composition

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