Structures where the injectivity of morphisms is forced Can someone give me some examples of mathematical structures where the associated morphisms are forced to be injective (e.g. fields)?
Thanks

Schur's lemma is a more broad result in this direction. The rule of thumb is that you know for a given category (of course, when applicable) what the kernel is going to look like, so if your object doesn't have nontrivial subobjects that look like that (like a field, or simple module) nonzero morphisms are going to be injective. 
