Implication Details
Assumptions: exact
Conclusions: left exact, right exact
This is an equivalence.
Proof: This holds by definition.
Show 27 functors using this implication
- abelianization functor for groups
- functor of continuous functions
- binary coproduct functor on sets
- countable copower functor on sets
- binary diagonal functor on the category of sets
- discrete topology functor
- doubling functor on sets
- enveloping group functor
- forgetful functor from abelian groups to groups
- forgetful functor from rings to monoids
- forgetful functor for groups
- forgetful functor from groups to monoids
- forgetful functor for rings
- forgetful functor for topological spaces
- forgetful functor for vector spaces
- free group functor
- group of units functor
- identity functor on the category of sets
- modulo p functor
- monoid ring functor
- p-torsion functor
- contravariant power set functor
- covariant power set functor
- binary product functor on sets
- sequences functor on sets
- squaring functor on sets
- torsion functor