Editing Subobject classifier (section)

=== Presheaves ===
Given a small category <math>C</math>, the category of [[presheaves]] <math>\mathrm{Set}^{C^{op}}</math> (i.e. the [[functor category]] consisting of all contravariant functors from  <math>C</math> to <math>\mathrm{Set}</math>) has a subobject classifer given by the functor sending any <math>c \in C</math> to the set of [[Sieve (category theory)|sieves]] on <math>c</math>. The classifying morphisms are constructed quite similarly to the ones in the sheaves-of-sets example above.