Talk:Full and faithful functors

Examples[edit]

It says "The forgetful functor U : Grp → Set is faithful but neither injective on objects or morphisms."

I am suspicious of that grammar, but as I do not know whether "neither injective" is a technical term for a variant of or method of injection I do not dare try to rephrase it. I am suspecting though that maybe it might be intending to say something along the lines of "is faithful but it is injective on neither objects nor morphisms" or "is faithful, but on objects and on morphisms it is not injective". Its a hard call to make as to which construction is clearest, its a tricky statement to try to write.

Knotwork 15:16, 24 August 2006 (UTC)[reply]

This examples sections needs an urgent revision. Albmont (talk) 12:22, 30 June 2009 (UTC)[reply]

The grammar question is irrelivant as it occurs in the midst of making a false claim; by very definition, every faithful functor induces an injective map on Hom sets........ —Preceding unsigned comment added by 128.101.152.25 (talk) 16:47, 4 August 2009 (UTC)[reply]

The second example is not full[edit]

Specifically, there are no functions from a nonempty set to the empty set, so nothing in that (empty!) hom-class gets mapped to the sole morphism of that image. This can be fixed by mapping every nonempty set to some singleton (like {{}}, which is the most obvious choice) and the empty set to itself, the morphisms can then be mapped in the obvious way. Someone who's a better writer than me should revise it. 166.137.208.21 (talk) 20:14, 9 December 2013 (UTC)[reply]

First sentence: what does "resp." mean[edit]

The author perhaps meant "respectively", and if so, please spell it out. Better yet, just write two sentences instead of one. Gwideman (talk) 06:37, 17 December 2014 (UTC)[reply]