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  "body": "\n## Summary\n\nA morphism of schemes is a morphism of [[locally ringed spaces|B7FPT8JTXR]] between [[schemes|5A35TYZD02]].\nIt is a continuous map together with a compatible way to pull back functions.\nBetween [[affine schemes|B3V3XJ2W8G]], morphisms are the same as ring homomorphisms in the opposite direction.\nSchemes with these morphisms form a category, the setting for almost all constructions of algebraic geometry.\n\n## Explanations\n\n### L1 human\n\nA map between two geometric objects should send points to points and also let functions be pulled back.\nFor schemes, the second part is part of the data: a function $g$ on an open set of the target becomes a function on its preimage.\nThe local condition says that if $g$ vanishes at $f(x)$, then its pullback vanishes at $x$.\nFor example, the ring inclusion $\\Z \\to \\Z[i]$ gives a morphism $\\operatorname{Spec} \\Z[i] \\to \\operatorname{Spec} \\Z$, which sends a prime ideal of $\\Z[i]$ to its intersection with $\\Z$.\n",
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