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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]]
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