Definition of "descends to"

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My textbook keeps saying that maps "descend to" other maps. I have never encountered this terminology before (at least not in English). What does it mean?

Here is an example:

The function $H$ is a smooth invariant function on $M = \mathbb{C}^2$, and therefore descends to a smooth function on $M_0$.

In general, how do I interpret "descends to"?

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1 Answer

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It usually has the same meaning as "induces a function on". It is often used in connection with the universal property of a quotient (group/space/etc.), which explains the "descend".

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