# Differences

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faithful_functor [2015/04/17 10:31] (current) nikolaj created |
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+ | ===== Faithful functor ===== | ||

+ | ==== Collection ==== | ||

+ | | @#FFBB00: definiendum | @#FFBB00: $F$ in it | | ||

+ | | @#AAFFAA: inclusion | @#AAFFAA: $F:{\bf C}\longrightarrow{\bf D}$ | | ||

+ | | @#AAFFAA: inclusion | @#AAFFAA: ${\bf C},{\bf D}$ ... locally small | | ||

+ | | @#55EE55: postulate | @#55EE55: $\mathrm{fmap}(F)_{X,Y}:{\bf C}[X,Y]\to{\bf D}[FX,FY]$ ... injective | | ||

+ | >Here I needed to introduc the notation $\mathrm{fmap}(F)_{X,Y}$ for the polymorphic function at $X$ and $Y$ | ||

+ | |||

+ | ----- | ||

+ | === Reference === | ||

+ | Wikipedia: | ||

+ | [[http://en.wikipedia.org/wiki/Faithful_functor|Faithful functor]] | ||

+ | |||

+ | ----- | ||

+ | === Subset of === | ||

+ | [[Functors]] | ||

+ | === Requirements === | ||

+ | [[Locally small category]] |