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[curry-howard] Re: unicity of arrows #1
Hi, nice blog post.
Two nitpicks though.
Nitpick 1: t' should probably be a T -> (AxB)xC since it is called an arrow.
Nitpick 2: t' is not necessarily unique: there are as many arrows from T to (AxB)xC as there are members of this object. There is only one that makes some diagram (involving t) commute, though. I get what you meant but the wording is maybe a bit misleading to category theory newcomers.
Nitpick 1: You are correct.
You're right that there are as many arrows from T to (AxB)xC as there are elements in it, but that might be zero. It would be the case if, for instance, C were empty. But then Ax(BxC) would be empty too, and we wouldn't have the starting arrow for the proof.