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subobject_classifier [2015/03/22 01:37] nikolaj |
subobject_classifier [2015/04/12 15:38] nikolaj |
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=== Elaboration === | === Elaboration === | ||
- | The postulate says that for any given mono $m_S$ from $S$ to $X$, there is a unique arrow $\chi_S$ from $X$ to the domain of $\top$, such that the following is a [[pullback . category theory|pullback]] diagram | + | The postulate says that for any given mono $m_S$ from $S$ to $X$, there is a unique arrow $\chi_S$ from $X$ to the domain $\Omega$ of $\top$, such that the following completes to a [[pullback . category theory|pullback]] diagram |
$$ | $$ | ||
Line 61: | Line 61: | ||
\begin{CD} | \begin{CD} | ||
- | \varepsilon_A @>{!_S}>> \{0\} | + | \varepsilon_A @>{!}>> \{0\} |
\\ | \\ | ||
@VVV @VV{\top}V | @VVV @VV{\top}V |