- #1

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i.e. Xx{point} isomorphic to X

Thanks

- Thread starter Ad123q
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- #1

- 19

- 0

i.e. Xx{point} isomorphic to X

Thanks

- #2

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Anytime the objects in the product are pairs of objects from the factors, and the second coordinate is always the same. Then the isomorphism is just projection onto the first coordinate, which has as its inverse inclusion into the product.

- #3

Landau

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Let the two projections [itex]\pi_A:A\to A[/itex] and [itex]\pi_\star:A\to \star[/itex] be the identity and the unique one, respectively. Now suppose Z is any object with arrows [itex]p_A:Z\to A[/itex] and [itex]p_\star:Z\to \star[/itex]. Then there is indeed a unique arrow [itex]u:Z\to A[/itex] such that [itex]\pi_A\circ u=p_A[/itex] and [itex]\pi_\star\circ u=p_\star[/itex]: it is of course u=p_A!

So [tex]A\times\star\cong A[/tex].

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