Terminology Archive
Conservative fucntor
A functor F:C→D is conservative if it is “isomorphism-reflecting”, i.e. if g:a→b is a morphism in C such that F(g) is an isomorphism in D, then g is an isomorphism in C.
Remarks
Sometimes conservative functors are assumed to be faithful as well. If C has, and F preserves, equalizers, then conservativity implies faithfulness.
http://ncatlab.org/nlab/show/conservative+functor
Every coequalizer is an epimorphism
http://en.wikipedia.org/wiki/Epimorphism
A functor F:C→D is conservative if it is “isomorphism-reflecting”, i.e. if g:a→b is a morphism in C such that F(g) is an isomorphism in D, then g is an isomorphism in C.
Remarks
Sometimes conservative functors are assumed to be faithful as well. If C has, and F preserves, equalizers, then conservativity implies faithfulness.
http://ncatlab.org/nlab/show/conservative+functor
Every coequalizer is an epimorphism
http://en.wikipedia.org/wiki/Epimorphism
