Let us consider an example of a '''subobject classifer''' in the [['''[[Topos of presheafs]]''']] <math>\mathcal{S}^{C^{op}}</math>. The formal definition goes as follows
'''Definition''':
A '''Subobject Classifier''' <math>\Omega</math> is a [[presheaf]]
<math>\Omega:''C''\rightarrow\mathcal{S}^{''C''^{op}}</math> such that to each object <math>A\in'' C''</math>
there corresponds an object <math>\Omega(A)\in\mathcal{S}^{''C''^{op}}</math> which represents the set
of all sieves
on A, and to each
''<math>C''</math>-arrow <math>f:B\rightarrow A</math> there corresponds an
<math>\mathcal{S}^{''C''^{op}}-arro</math> \Omega(f):\Omega(A)\rightarrow\Omega(B)</math> such that
<math>\Omega(f)(S):=\{h:''C''\rightarrow B|f o h\in S\}</math> is a sieve on B, where <math>\Omega(f)(S)\equiv f^*(S)</math>
