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A strange formulation

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I quote: "In other words, is injective iff any -morphism into extends (via composition on the left) to a morphism into ."

A morphism into extends to a morphism into ? 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

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We have at least 3 symbols to denote a category: 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 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 , which are widely used for denoting complex numbers. I do not like 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 (in latex). This would be coherent with most well presented mathematical articles. D.Lazard (talk) 16:52, 1 September 2018 (UTC)[reply]