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Stream: learning: questions

Topic: Nathaniel Osgood: pushouts and monos

John Baez (Jun 10 2024 at 13:15):

My friend @Nathaniel Osgood has a question, which I will ask for him to demonstrate how asking questions works here.

Suppose we have a pushout square involving morphisms $f: A \to B$, $g: A \to C$, $h: B \to D$, $k: C \to D$. Suppose $g, h$ and $k$ are monos. Does $f$ need to be monic?

He is particularly interested in the case where this pushout square is in a presheaf category. Does that help?

Ralph Sarkis (Jun 10 2024 at 13:23):

For reference:
image.png

Kalin Krishna (Jun 10 2024 at 13:39):

I don't know whether I misunderstood the question somehow, but since the square commute, isn't $h\circ f$ monomorphism and hence $f$ mono?

John Baez (Jun 10 2024 at 14:31):

Nice. You didn't misunderstand it. Instead of trying to think about it myself, I just wanted to post it here so @Nathaniel Osgood could see how to ask questions here, and see that it works.