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pairing — pretty simple, but not to be confused with the product
copairing, with examples at interval object.
domain, as disambiguation
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<a href="https://ncatlab.org/nlab/show/copairing">copairing</a>
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<p>Thanks. Reminds me that I don't have the font installed that you use for the coproduct...</p>
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<a href="https://ncatlab.org/nlab/show/pairing">pairing</a> — pretty simple, but not to be confused with the product
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<p>Was that a hind in my direction, yb the way? I think I may have written "product" for "pairing" here and there. Not that I can't tell one from the other, but maybe I was not using good terminology.</p>
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It wasn't meant to be a hint, but I wrote it to link it from interval object, where you had not only written ‘product’ for ‘pairing’ but had also denoted copairing as if it were a coproduct.
But I fixed all that.
Do you mean writing ? Isn't that standard notation?
It's not the standard that I'm aware of.
If and , then .
But if is the same as , then we also have .
The relation between these (or rather, their duals) is discussed in detail at pairing.
There are lots of notations for the copairing and I suppose that somebody might write it as , but that conflicts with the idea that is a functor, which is reflected in my . Of course, if you keep track of the targets, then there's no actual conflict, but it doesn't seem right to me.
I'm not sure that there is a strong consensus on notation here; my own has been to use for pairing and for copairing. Like Toby, I would reserve (or more often just ) for the bifunctor.
Wait: how do I activate LaTeX formulas here again? [Note: I've edited after figuring this out]
Okay, testing...
Okay.
I agree that there's no consensus on notation, but I also agree that or should be reserved for the bifunctor.
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