Item 8 (00W4) — The Clowder Project

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*To be replaced with Linus Romer's Elemaints when it is released.

Descending Functions to Quotient Sets, V. Let $R$ be an equivalence relation on $X$. If the conditions of Item 4 hold, then the following conditions are equivalent:
1. The map $f\colon X\to Y$ is surjective.
2. The map $\overline{f}\colon X/\mathord {\sim }_{R}\to Y$ is surjective.

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