Definitions for "Morphism"
Substitution s - in particular 1dim substitutions - with prototile s can be formulated as a endomorphism of the free group with generators. If the endomorphism is an automorphism, i.e., if it is invertible, then the substitution is also called invertible.
A mapping between two mathematical objects of the same type, such as topological spaces or groups, that preserves the essential structure of the object.
a function from A to B that captures at least part of the essential nature of the set A in its image in B
a labeled, directed connection from one object to another, like a directed arc in a digraph