Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision Last revision Both sides next revision | ||
subobject_classifier [2015/03/22 01:38] nikolaj |
subobject_classifier [2015/10/20 18:26] nikolaj |
||
---|---|---|---|
Line 55: | Line 55: | ||
$x\in S\leftrightarrow \langle S,x\rangle\in \varepsilon_A$, | $x\in S\leftrightarrow \langle S,x\rangle\in \varepsilon_A$, | ||
- | where $\varepsilon_A \subseteq {\mathcal P}(X)\times X$. As a power set ${\mathcal P}(X)$ in bijection with the space of characteristic functions ${\mathrm{Hom}}(X,\{0,1\})=\{0,1\}^X$, the "is element of"-relation can be defined as the following pullback: | + | where $\varepsilon_A \subseteq {\mathcal P}(X)\times X$. As a power set ${\mathcal P}(X)$ is in bijection with the space of characteristic functions ${\mathrm{Hom}}(X,\{0,1\})=\{0,1\}^X$, the "is element of"-relation can be defined as the following pullback: |
$$ | $$ | ||
Line 61: | Line 61: | ||
\begin{CD} | \begin{CD} | ||
- | \varepsilon_A @>{!_S}>> \{0\} | + | \varepsilon_A @>{!}>> \{0\} |
\\ | \\ | ||
@VVV @VV{\top}V | @VVV @VV{\top}V |