Talk:Injective object

A strange formulation

I quote: "In other words, $Q$ is injective iff any ${\mathcal {H}}$ -morphism into $Q$ extends (via composition on the left) to a morphism into $Q$ ."

A morphism into $Q$ extends to a morphism into $Q$ ? Can someone formulate this more clearly? I cannot, since I am in the process of learning category theory myself, so I do not know what the correct formulation is.78.143.70.6 (talk) 17:40, 27 August 2015 (UTC)[reply]

The wording may be a bit unfortunate (it's correct though). I have added a diagram, from the corresponding better-written German article, which should help. -- Taku (talk) 21:52, 27 August 2015 (UTC)[reply]

Inconsistent notation for the category C

We have at least 3 symbols to denote a category: C, ${\mathfrak {C}}$ , $\mathbf {C}$ . Does it make sense to use one of them consistently? --Shiyu Ji (talk) 16:29, 1 September 2018 (UTC)[reply]

So far it is most convenient to use ${\mathfrak {C}}$ to be consistent. --Shiyu Ji (talk) 16:41, 1 September 2018 (UTC)[reply]

{{ec} It is a good idea of homogenizing notation. Personally, I oppose to C and

\mathbf {C}

, which are widely used for denoting complex numbers. I do not like

{\mathfrak {C}},

which may a source of confusion for a user who has never encountered this font. Thus, I suggest to use

C

(for isolated occurrences),

C

(inside html formulas) and

C

(in latex). This would be coherent with most well presented mathematical articles. D.Lazard (talk) 16:52, 1 September 2018 (UTC)[reply]