Implication Details
Claim: If a functor is fully faithful, then it is conservative.
Proof: If is an isomorphism, its inverse has the form since is full. Since is faithful, it follows that is inverse to .
Show 22 functors using this implication
- discrete topology functor
- empty functor to the category of sets
- forgetful functor from abelian groups to groups
- forgetful functor from commutative rings to rings
- forgetful functor from finite sets to sets
- forgetful functor from finite abelian groups to abelian groups
- forgetful functor from finite groups to groups
- forgetful functor from Hausdorff spaces to topological spaces
- forgetful functor from groups to monoids
- forgetful functor for topological spaces
- forgetful functor from torsion abelian groups to abelian groups
- forgetful functor from torsion-free abelian groups to abelian groups
- identity functor on the category of sets
- inclusion functor from extended natural numbers to ordinal numbers
- indiscrete topology functor
- nerve functor
- opposite category functor
- opposite monoid functor
- span endpoints inclusion
- trivial functor from the walking idempotent
- walking isomorphism object inclusion
- walking morphism representation