Suppose we are in a category with morphisms $f,g$ such that $g$ and $fg$ are monomorphisms. Is $f$ also a monomorphism? How do you prove this, assuming it is correct? (which it feels like it should be)
Tell me more
×
Mathematics Stack Exchange is a question and answer site for
people studying math at any level and professionals in related fields. It's 100% free, no registration required.
|
|
|
No, not necessarily. Since $fg$ mono implies $g$ mono (check!), you're essentially asking if "$fg$ mono implies $f$ mono", which is easily seen to be false, e.g. in $\mathrm{Set}$. |
|||
|
|
