Implication Details
Assumptions: pointed, strict initial object
Conclusions: trivial
Reason: If is the zero object, then for every object the unique morphism is an isomorphism by assumption.
Show 19 categories using this implication
- category of abelian groups
- category of finitely generated abelian groups
- category of compact Hausdorff spaces
- category of finite abelian groups
- category of finite ordered sets
- category of finite sets
- category of free abelian groups
- category of metric spaces with non-expansive maps
- poset of natural numbers
- category of pseudo-metric spaces with non-expansive maps
- category of left modules over a ring
- category of left modules over a division ring
- category of pointed sets
- category of abelian sheaves
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- walking span
- walking splitting