Implication Details
Claim: A category is pointed if and only if it has a terminal object and has zero morphisms.
Proof: This follows from the dual implication.
This implication has a dual.
Show 21 categories using this implication
- category of Banach spaces with linear contractions
- category of commutative monoids
- simplex category
- category of finite groups
- category of finite sets of even cardinality
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- category of fields of characteristic zero
- category of groups
- category of monoids
- partially ordered collection of ordinal numbers
- category of partially ordered sets without isolated points
- category of sets and relations
- category of rngs
- category of pointed sets
- category of large families of sets which are mostly empty
- category of non-empty sets
- category of pointed topological spaces
- category of large vector spaces over a large field with a small basis
- walking coreflexive pair
- walking splitting