[[!redirects monic]] [[!redirects monomorphism]] [[!redirects n-monic]] [[!redirects n-monomorphism]] [[!redirects n-monic function]] ## Definition ## Given a natural number $n:\mathbb{N}$, a function $f:A \to B$ is a __$n$-monic function__ if for all terms $b:B$ the [[homotopy fiber]] of a function $f:A \to B$ over $b:B$ has an [[homotopy level]] of $n$. $$isMonic(n, f) \coloneqq hasHLevel\left(n, \prod_{b:B} hFiber(f, b)\right)$$ A [[homotopy equivalence]] is a $0$-monic function. $1$-monic functions are typically just called __monic__ functions. ## See also ## * [[homotopy fiber]] * [[epic function]]