11. A strong monomorphism satisfies a certain lifting property with respect to commutative squares involving an epimorphism. 12. Eventually the monomorphism concept of Louis Pasteur was accepted by the scientific community in the 1950s. 13. A "'split monomorphism "'is an homomorphism that has a right inverse. 14. In short, the property of being a monomorphism is dual to the property of being an epimorphism. 15. In many categories it is possible to write every morphism as the composition of an epimorphism followed by a monomorphism . 16. This is also an example of a ring homomorphism which is both a monomorphism and an epimorphism, but not an isomorphism. 17. In the context of abstract algebra or universal algebra, a "'monomorphism "'is an injective homomorphism. 18. For sets and vector spaces, every monomorphism is a split homomorphism, but this property is wrong for most common algebraic structures. 19. For example, whether or not a morphism of sheaves is a monomorphism , epimorphism, or isomorphism can be tested on the stalks. 20. :Wouldn't an " isomorphism into " a group just be a monomorphism ( i . e . an injective homomorphism )?
