"Isomorphy" in mathematical texts

Question

I want to use the term "isomorphy" in a mathematical text, like:

There is isomorphy of objects A, B, C, D, E and F.

which is equivalent to

There exist isomorphisms between the objects A, B, C, D, E and F.

or

The objects A, B, C, D, E and F are pairwise isomorphic.

I know that these sentences mean more or less the same, but the first sentence captures more my message. But it seems that in mathematical English, "isomorphy" is not a term that common in this sense. Will I still be understood with this terminology, and should I adopt it?

Addendum: In my opinion, "isomorphic" is a pairwise relation, whereas "isomorphism" is the concrete morphism between two isomorphic objects, of which there might be many. "Isomorphy" does not decide on the particular isomorphism, and shifts the focus from the pairwise relation to the "big picture". In German those three terms are clearly distinguished and used. To me, it appears bizarre that English lacks this usage.

IMHO, I feel like this would be more suited for Mathematics SE. — , Oct 20 '14 at 15:24
I there is common agreement on that, can feel free to migrate it. — shuhalo, Oct 20 '14 at 15:29
You'll probably need a moderator to move it to another Stack Exchange. Alternatively, you can copy the question, delete this version, and just open a new question there. Since you already have 500 rep on this SE, you'll start with 101 rep in Mathematics if you don't have an account there. — , Oct 20 '14 at 15:30
Closely related: What word means "the property of being holomorphic"? — Nate Eldredge, Oct 21 '14 at 01:21

score 7 · Answer 1 · answered Oct 20 '14 at 16:27

7

No, "isomorphy" is very uncommon in contemporary mathematical English.

You should just say, e.g. "The objects A,B,C,D,E,F are all isomorphic".

I don't really understand how your suggested first sentence could capture your message any better than this. If I myself understand what you intend "isomorphy" to mean, all of the suggested sentences mean exactly the same thing. In terms of "capturing your message", that cannot be done by using words that the majority of your readers will not know. Still, if there is some nuance of meaning I am missing, I would be interested to hear it.

answered Oct 20 '14 at 16:27

Pete L. Clark

97,892

I have added an explanation. – shuhalo Oct 20 '14 at 18:23
Languages are funny things, and people tend to say things the way their language allows. Japanese, as I understand it, doesn't have articles or plurals. I believe Japanese people are happy expressing what they need in other ways, until they try to use English. Meanwhile English people can't understand why nouns should have gender, or why you would have neuter ones. – Jessica B Oct 20 '14 at 20:00
2

I don't really understand why you feel that the pairwise aspect is significant. "Has the same color" is a pairwise relation, but we happily extend it to sets of objects. This is a general property of equivalence relations. If you want a noun for the common property that a class of isomorphic objects (in a category, say) share: sorry, I am not aware of a graceful way to say this in English. You could say that the objects lie in the same isomorphism class, but that's significantly more complicated than saying they are isomorphic. – Pete L. Clark Oct 21 '14 at 01:15

"Isomorphy" in mathematical texts

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