Hi, I know that if I have a monomorphism [itex]f:X\rightarrow Y [/itex] then for any arrows [itex]g,h:A \rightarrow X[/itex] we have [itex]f \circ g = f \circ h \; \Rightarrow \; g=h [/itex](adsbygoogle = window.adsbygoogle || []).push({});

However in a topological space, if I have [itex]f[/itex] to be an injection but now have [itex]f \circ g \simeq f \circ h[/itex] (where [itex]\simeq[/itex] denotes homotopic) then does this imply that [itex]g \simeq h[/itex]?

So my question is, is this true? If not what conditions would I require to make it true?

Thanks,

Tom

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# Monomorphism cancellation property

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