===== Presheaf category =====
==== Category ====
| @#55CCEE: context     | @#55CCEE: ${\bf C}$ ... small category |
| @#FFBB00: definiendum | @#FFBB00: ${\bf Set}^{{\bf C}^\mathrm{op}}$ |

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The co- and contravariant hom-functors $\mathrm{Hom}(B,-)$ and $\mathrm{Hom}(-,B)$ are maybe the most natural functors. While forgetful functors are other examples of covariant set-valued functors, covariant functors very often have to do with function spaces. (Once we pass from presheaves to sheaves by adding some more "topological requirements", this becomes a theorem: sheaves can always be viewed as evaluating to collections of function spaces.)

=== Reference ===
Wikipedia: 
[[http://en.wikipedia.org/wiki/Yoneda_lemma|Yoneda lemma]],
[[http://en.wikipedia.org/wiki/Functor_category|Functor category]]

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=== Subset of ===
[[Functor category]]
=== Context ===
[[Cat]]
=== Requirements ===
[[Set]], [[Opposite category]]