Scrabble?! MONOMORPHISMS

Definitions of MONOMORPHISMS in various dictionaries:

In the context of abstract algebra or universal algebra, a monomorphism is an injective homomorphism. A monomorphism from X to Y is often denoted with the notation X ↪ Y. In the more general setting of category theory, a monomorphism (also called a monic morphism or a mono) is a left-cancellative morphism, that is, an arrow f : X → Y such that, for all morphisms g1, g2 : Z → X, f ∘ g 1 = f ∘ g 2 ⇒ g 1 = g 2 . {\displaystyle f\circ g_{1}=f\circ g_{2}\Rightarrow g_{1}=g_{2}.} Monomorphisms are a categorical generalization of injective functions (also called "one-to-one functions"); in some categories the notions coincide, but monomorphisms are more general, as in the examples below. The categorical dual of a monomorphism is an epimorphism, i.e. a monomorphism in a category C is an epimorphism in the dual category Cop. Every section is a monomorphism, and every retraction is an epimorphism.