Implication Details
Claim: A functor is essentially surjective and is fully faithful if and only if it is an equivalence.
Proof: This is standard, see Mac Lane, Ch. IV, Theorem 4.1.
Show 35 functors using this implication
- abelianization functor for groups
- binary coproduct functor on sets
- binary diagonal functor on the category of sets
- countable copower functor on sets
- discrete topology functor
- doubling functor on sets
- enveloping group functor
- forgetful functor for groups
- forgetful functor for rings
- forgetful functor for topological spaces
- forgetful functor for vector spaces
- forgetful functor from abelian groups to groups
- forgetful functor from groups to monoids
- forgetful functor from groups to pointed sets
- forgetful functor from rings to monoids
- functor of continuous functions
- fundamental group functor
- group of units functor
- identity functor on the category of sets
- indiscrete topology functor
- modulo p functor
- monoid ring functor
- opposite category functor
- opposite monoid functor
- p-torsion functor
- path components functor
- sequences functor on sets
- simple-group probing functor
- squaring functor on sets
- torsion functor
- trivial functor from the category of groups
- trivial functor from the category of sets
- trivial functor from the delooping
- trivial functor from the walking idempotent
- walking isomorphism object inclusion