Presheaves


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Presheaves

Definition 3.7   A presheaf on a small3.1 category $ \mathscr{C}$ is a contravariant functor $ X:\mathscr{C}\rightarrow S$ form $ \mathscr{C}$ to the category of sets S

Example 3.1   An example of a presheaf X on a category $ \mathscr{C}$ is:

$\displaystyle \xymatrix{
 &&1&&\\
 A\ar[rru]^h&&&&B\ar[llu]_g\\
 &&o\ar[rru]_f\ar[llu]^k&&\\
 &&\Downarrow^X&&\\
 &&X(1)\ar[rrd]^{X(g)}\ar[lld]_{X(h)}&&\\
 X(A)\ar[rrd]_{X(k)}&&&&X(B)\ar[lld]^{X(f)}\\
 &&X(0)&&\\
 }$



Cecilia Flori 2007-01-02