Morphisms
A monoid morphism f from a free monoid B∗ to a monoid M is a map such that f(xy) = f(x)⋅f(y) for words x,y and f(ε) = ι. The morphism f is determined by its values on the letters of B and conversely any map from B to M extends to a morphism. A morphism is non-erasing or continuous if no letter of B maps to ι and trivial if every letter of B maps to ι.
A morphism f from a free monoid B∗ to a free monoid A∗ is total if every letter of A occurs in some word in the image of f; cyclic if the image of f is contained in w∗ for some word w of A∗. A morphism f is k-uniform if the length |f(a)| is constant and equal to k for all a in A. A 1-uniform morphism is strictly alphabetic or a coding.
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