Faithful functor

Collection

definiendum $F$ in it
inclusion $F:{\bf C}\longrightarrow{\bf D}$
inclusion ${\bf C},{\bf D}$ … locally small
postulate $\mathrm{fmap}(F)_{X,Y}:{\bf C}[X,Y]\to{\bf D}[FX,FY]$ … injective
Here I needed to introduc the notation $\mathrm{fmap}(F)_{X,Y}$ for the polymorphic function at $X$ and $Y$

Reference

Wikipedia: Faithful functor


Subset of

Functors

Requirements

Locally small category