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this should read "the kernel of the morphism of groups always CONTAINS", as the subject (the kernel) is singular.
Well, as you note, a morphism in the category of groups is a mapping from one group to another, so it makes sense to speak of a "morphism of (two) groups."
However, I don't think it is correct to use the definite article here, as there can be multiple different morphisms.
The French sentence and its German translation use indefinite articles. Not sure about Italian.
So I propose to change
the morphism → a morphism
They say "morphism" in category theory, but one probably shouldn't speak of elements or necessarily only of groups in that context. I think "group homomorphism" is the word of choice here. That is a structure-preserving map. I've just gone ahead and changed the sentence as it is unowned. Maybe one of our natives will feel comfortable to adopt it.
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This sentence was initially added as a translation of sentence #696315
The kernel of the morphism of groups always contain neutral element.
added by boracasli, January 4, 2011
linked by boracasli, January 4, 2011
The kernel of the morphism of groups always contains the neutral element.
edited by Nero, October 2, 2011
linked by Guybrush88, June 26, 2014
The kernel of a group homomorphism always contains the neutral element.
edited by Pfirsichbaeumchen, October 2, 2019
linked by Pfirsichbaeumchen, October 2, 2019
linked by Pfirsichbaeumchen, October 2, 2019
linked by MacGyver, October 2, 2019
linked by Thanuir, October 4, 2019
linked by al42and, November 28, 2023
