Implication Details
Claim: If a functor is a coreflector, then it preserves initial objects.
Proof: This follows from the dual implication.
This implication has a dual.
Show 15 functors using this implication
- forgetful functor from rings to monoids
- forgetful functor for groups
- forgetful functor for rings
- forgetful functor for topological spaces
- forgetful functor for vector spaces
- group of units functor
- identity functor on the category of sets
- opposite category functor
- opposite monoid functor
- contravariant power set functor
- covariant power set functor
- ring idempotents functor
- trivial functor from the category of groups
- trivial functor from the category of sets
- walking isomorphism object inclusion