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  "body": "\n## Summary\n\nA semiconjugacy from one dynamical system to another is a continuous surjection that intertwines the two maps.\nThe target system is then called a factor of the source, and the source an extension of the target.\nThe map itself is a factor map.\nA factor is a simplified picture of the system that may forget some information.\nStill, every orbit of the factor is the image of an orbit of the extension.\nA semiconjugacy that is a homeomorphism is a [[topological conjugacy|HNXXAPQKG3]]; the same idea with measure-preserving maps gives factors in ergodic theory.\n\n## Explanations\n\n### L1 human\n\nA factor map is like a blurry camera filming a system: it may merge different states, but it is faithful to the motion.\nWatching the blurry film step by step is the same as filming each step of the real system.\nFor example, write a number in $[0, 1)$ in binary and shift the digits one place to the left.\nReading the digits as a number turns this shift into the doubling map $x \\mapsto 2x \\bmod 1$, so the doubling map is a factor of the shift.\n",
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