Implication Details
Assumptions: Grothendieck abelian, self-dual
Conclusions: trivial
Proof: This follows since the dual of a non-trivial Grothendieck abelian category cannot be Grothendieck abelian. See Peter Freyd, Abelian categories, p. 116.
Show 11 categories using this implication
- category of abelian sheaves
- category of finite-dimensional vector spaces [countable field]
- category of finite-dimensional vector spaces [uncountable field]
- delooping of a non-trivial finite group
- delooping of an infinite countable group
- delooping of an infinite uncountable group
- delooping of the additive monoid of natural numbers
- poset [0,1]
- walking commutative square
- walking composable pair
- walking morphism