tom.coyne
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Hi, I know that if I have a monomorphism f:X\rightarrow Y then for any arrows g,h:A \rightarrow X we have f \circ g = f \circ h \; \Rightarrow \; g=h
However in a topological space, if I have f to be an injection but now have f \circ g \simeq f \circ h (where \simeq denotes homotopic) then does this imply that g \simeq h?
So my question is, is this true? If not what conditions would I require to make it true?
Thanks,
Tom
However in a topological space, if I have f to be an injection but now have f \circ g \simeq f \circ h (where \simeq denotes homotopic) then does this imply that g \simeq h?
So my question is, is this true? If not what conditions would I require to make it true?
Thanks,
Tom