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3.Preserves and Reflects

11.06.2020

Contents/Index

1.Definition
2.Full and Faithful
@3.Preserves and Reflects
4.Contra-, Co- and Bivariant
5.Co- and Contravariant Hom Functors

Given two categories $\mathcal{C},\mathcal{D}$, and a functor $F : \mathcal{C} \rightarrow \mathcal{D}$, we say that $F$

  • preserves a propery $P$ if whenever an object or arrow, $c$, of $\mathcal{C}$ has $P$, then so does $F(c)$.
  • reflects a property $P$ if whenever an object or arrow, $d = F(c)$, of $\mathcal{D}$ has $P$, then so does $c$.
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