Implication Details
Claim: If a category is pointed and has a strict initial object, then it is trivial.
Proof: If is the zero object, then for every object the unique morphism is an isomorphism by assumption.
Show 23 categories using this implication
- category of abelian groups
- category of finitely generated abelian groups
- category of Banach spaces with linear contractions
- category of cochain complexes of abelian groups
- category of compact Hausdorff spaces
- category of filtered vector spaces
- category of finite abelian groups
- category of free abelian groups
- partially ordered set of natural numbers
- category of left modules over a ring
- category of left modules over a division ring
- category of left modules over a non-semisimple ring
- category of sequences of abelian groups
- category of pointed sets
- category of abelian sheaves
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of uniform spaces
- category of vector spaces
- category of graded abelian groups
- category of graded modules over a graded ring
- walking span
- walking splitting