Implication details
Claim: If a category is one-way and has zero morphisms, then it is thin.
Proof: If are two morphisms, then since we have
Show 20 categories using this implication
- category of finitely generated abelian groups
- category of Banach spaces with linear contractions
- category of commutative monoids
- category of finite abelian groups
- category of finite groups
- category of finite-dimensional vector spaces
- category of finite-dimensional vector spaces [countable field]
- category of finite-dimensional vector spaces [finite field]
- category of finite-dimensional vector spaces [uncountable field]
- category of finitely generated free abelian groups
- category of groups
- category of countable groups
- category of finitely generated groups
- category of monoids
- category of finitely generated projective modules over the ring of dual numbers
- category of pointed sets
- category of pointed topological spaces
- category of long transfinite sequences of abelian groups
- category of countable-dimensional vector spaces
- category of large families of vector spaces which are mostly zero