Implication Details
Claim: If a category is left cancellative and has zero morphisms, then it is thin.
Proof: If are two morphisms, then , so that .
This implication has a dual.
Show 32 categories using this implication
- category of abelian groups
- category of large families of abelian groups
- category of finitely generated abelian groups
- category of finite sets and bijections
- delooping of a group
- delooping of an infinite countable group
- delooping of a non-trivial finite group
- delooping of an infinite uncountable group
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- category of cochain complexes of abelian groups
- 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 fields
- category of fields of characteristic zero
- category of free abelian groups
- category of finitely generated free abelian groups
- category of finitely generated projective modules over the ring of dual numbers
- category of left modules over a non-semisimple ring
- category of sequences of abelian groups
- category of abelian sheaves
- 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
- category of large vector spaces over a large field with a small basis
- forked commutative square
- category of graded abelian groups
- walking splitting