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icantadd
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I have a general sort of structural question. I have been reading a lot of maths papers lately, and it seems there are some isomorphisms that people omit from their calculations. For example, in a category with a terminal object, 1,
A \cong A \times 1
where the isomorphism is given from left to right by \langle 1_A , !_A \rangle where ! is the unique map into the terminal object, and the isomorphism from right to left is (left) projection. Now, let a : 1 \to A; an example of the abuse of notation I have seen quite often is to regard
\langle a , 1_1 \rangle : 1 \to A \times 1 as just a
Are there any obvious problems with making such an association? Are there any non-obvious problems with making such an association? Am I missing something?
A \cong A \times 1
where the isomorphism is given from left to right by \langle 1_A , !_A \rangle where ! is the unique map into the terminal object, and the isomorphism from right to left is (left) projection. Now, let a : 1 \to A; an example of the abuse of notation I have seen quite often is to regard
\langle a , 1_1 \rangle : 1 \to A \times 1 as just a
Are there any obvious problems with making such an association? Are there any non-obvious problems with making such an association? Am I missing something?
