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cartesian_closed_category [2015/03/19 21:21] nikolaj |
cartesian_closed_category [2015/12/17 19:28] nikolaj |
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| | @#FFBB00: definiendum | @#FFBB00: ${\bf C}$ in it | | | @#FFBB00: definiendum | @#FFBB00: ${\bf C}$ in it | | ||
| | @#AAFFAA: inclusion | @#AAFFAA: ${\bf C}$ ... category | | | @#AAFFAA: inclusion | @#AAFFAA: ${\bf C}$ ... category | | ||
| - | | @#55EE55: postulate | @#55EE55: ${\bf C}$ has a terminal object $*$ | | + | | @#55EE55: postulate | @#55EE55: ${\bf C}$ has a terminal object | |
| - | | @#55EE55: postulate | @#55EE55: For all $X,Y\in{\bf C}$ the product $X\times Y$ exists | | + | | @#55EE55: postulate | @#55EE55: For all $X,Y\in{\bf C}$, the product $X\times Y$ exists | |
| | @#55EE55: postulate | @#55EE55: For all $Y\in{\bf C}$, the functor $-\times Y$ from ${\bf C}$ to ${\bf C}$ has a right adjoint | | | @#55EE55: postulate | @#55EE55: For all $Y\in{\bf C}$, the functor $-\times Y$ from ${\bf C}$ to ${\bf C}$ has a right adjoint | | ||
| ----- | ----- | ||
| + | === Discussion === | ||
| + | Remark/Reminder: | ||
| + | |||
| + | $((A\times Y)\to B)\cong(A\to B^Y)$ | ||
| === Reference === | === Reference === | ||
