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Inverse image functor
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<p>In mathematics, specifically in <a href="/facts/Algebraic_topology/2wA8yrjT">algebraic topology</a> and <a href="/facts/Algebraic_geometry/rh7RHVp3">algebraic geometry</a>, an inverse image functor is a <a href="/facts/Covariance_and_contravariance_of_functors/l2u3rIBE">contravariant</a> construction of <a href="/facts/Sheaf_(mathematics)/MM3hcRw4">sheaves</a>; here “contravariant” in the sense given a map f : X → Y {\displaystyle f:X\to Y} , the inverse image <a href="/facts/Functor/l2u3rIBE">functor</a> is a functor from the <a href="/facts/Category_(mathematics)/7WzxUThf">category</a> of sheaves on <i>Y</i> to the category of sheaves on <i>X</i>. The <a href="/facts/Direct_image_functor/z3mckxvp">direct image functor</a> is the primary operation on sheaves, with the simplest definition. The inverse image exhibits some relatively subtle features. </p>