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Fiber functor
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<p>Fiber functors in <a href="/facts/Category_theory/6zS3DXPa">category theory</a>, <a href="/facts/Topology/2EqW47cU">topology</a> and <a href="/facts/Algebraic_geometry/rh7RHVp3">algebraic geometry</a> refer to several loosely related <a href="/facts/Functor/l2u3rIBE">functors</a> that generalise the functors taking a <a href="/facts/Covering_space/bDRGasl7">covering space</a> π : X → S {\displaystyle \pi \colon X\rightarrow S} to the <i>fiber</i> π − 1 ( s ) {\displaystyle \pi ^{-1}(s)} over a point s ∈ S {\displaystyle s\in S} . </p>