Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | Next revision Both sides next revision | ||
|
dependent_product_functor [2015/08/17 14:44] nikolaj |
dependent_product_functor [2015/10/13 20:50] nikolaj |
||
|---|---|---|---|
| Line 32: | Line 32: | ||
| == Explanation starting from the exp-hom adjunction == | == Explanation starting from the exp-hom adjunction == | ||
| - | A function space $Y^X$ can be characterized by the isomorphism $(A\to Y^X)\cong((A\times X)\to Y)$. Setting $\theta'(\langle a,x\rangle):=\langle \theta(a),x\rangle$ lets us moreover identify $(A\times X)\to Y$ with the space of function from that $\theta':(A\times X)\to (Y\times X)$ with the additional requirement that the second component is mapped to itself. | + | A function space $Y^X$ can be characterized by the isomorphism $(A\to Y^X)\cong((A\times X)\to Y)$. |
| + | Let us moreover identify $(A\times X)\to Y$ with the space of function from that $(A\times X)\to (Y\times X)$ with the additional requirement that the second component is mapped to itself, i.e. according to the scheme | ||
| + | $\theta'(\langle a,x\rangle):=\langle \theta(a),x\rangle$. | ||
| Again, in diagrams: Functions in | Again, in diagrams: Functions in | ||
