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hom-set_adjunction [2016/02/11 13:15] nikolaj |
hom-set_adjunction [2016/02/11 13:22] nikolaj |
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| == Idea == | == Idea == | ||
| - | More generally, view the left adjoint $F$ as A-"thickening" of ist argument ($X$) and view $G$ as the A-indexing of aspects of it's argument $Y$. | + | More generally, |
| + | view the left adjoint $F$ as A-"thickening" of ist argument ($X$) and view $G$ as the A-indexing of aspects of it's argument $Y$. | ||
| + | |||
| + | If ${\bf C}\neq{\bf D}$, then viewing $G$ as indexing may be harder. | ||
| == Example from Algebra == | == Example from Algebra == | ||
| Line 70: | Line 73: | ||
| $(A\times Y^A)$ to $Y$. | $(A\times Y^A)$ to $Y$. | ||
| - | The first can only be | + | The first can only be a direct embedding |
| $\eta_Y(y):=\lambda a.\, \langle a,y\rangle$ | $\eta_Y(y):=\lambda a.\, \langle a,y\rangle$ | ||
| - | and the second | + | and the second is an evaluation |
| $\epsilon_Y(\langle a,f\rangle) := f(a)$ | $\epsilon_Y(\langle a,f\rangle) := f(a)$ | ||
