To go from that implication to the fact that " q " is a monomorphism, assume that for some morphisms, where " G " is some divisible group.
32.
The companion terms " monomorphism " and " epimorphism " were originally introduced by Nicolas Bourbaki; Bourbaki uses " monomorphism " as shorthand for an injective function.
33.
The companion terms " monomorphism " and " epimorphism " were originally introduced by Nicolas Bourbaki; Bourbaki uses " monomorphism " as shorthand for an injective function.
34.
Many common notions from mathematics ( e . g . surjective, injective, free object, representation, isomorphism ) are definable purely in category theoretic terms ( cf . monomorphism, epimorphism ).
35.
An extremal monomorphism is a monomorphism that cannot be nontrivially factored through an epimorphism : Precisely, if with " e " an epimorphism, then " e " is an isomorphism.
36.
An extremal monomorphism is a monomorphism that cannot be nontrivially factored through an epimorphism : Precisely, if with " e " an epimorphism, then " e " is an isomorphism.
37.
In a general setting, one considers a monomorphism f \ to \ widetilde f of a group of diffeomorphisms of X to a group of bundle automorphisms of a natural bundle T \ to X.
38.
The categorical dual of a monomorphism is an epimorphism, i . e . a monomorphism in a category " C " is an epimorphism in the dual category " C " op.
39.
The categorical dual of a monomorphism is an epimorphism, i . e . a monomorphism in a category " C " is an epimorphism in the dual category " C " op.
40.
This conflicts with the usual pattern, where genetic monogamy is linked to the characteristics of strong social pairing, essential paternal contributions to brood rearing, and to sexual monomorphism; characteristics exhibited by the yellow honeyeater.
