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In computer science, and in particular functional programming, a hylomorphism is a recursive function, corresponding to the composition of an anamorphism followed by a catamorphism. Fusion of these two recursive computations into a single recursive pattern then avoids building the intermediate data structure. This is an example of deforestation, a program optimization strategy. A related type of function is a metamorphism, which is a catamorphism followed by an anamorphism.
1 A linear map is a homomorphism that preserves the vector space structure, namely the abelian group structure and scalar multiplication. 2  The scalar type must further be specified to specify the homomorphism, e.g. every R-linear map is a Z-linear map, but not vice versa.ince inverses exist in G and H, one can show that the identity of G maps to the identity of H and that inverses are preserved. The algebraic structure to be preserved may include more than one operation, and a homomorphism is required to preserve each operation.