Implication Details
Claim: If a category is cocartesian coclosed and has a terminal object, then it has a strict terminal object.
Proof: This follows from the dual implication.
Show 27 categories using this implication
- category of abelian groups
- category of abelian sheaves
- category of Banach spaces with linear contractions
- category of commutative monoids
- category of countable groups
- category of filtered vector spaces
- category of finite abelian groups
- category of finite ordered sets
- 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 abelian groups
- category of free abelian groups
- category of left modules over a division ring
- category of left modules over a ring
- category of metric spaces with non-expansive maps
- category of non-empty sets
- category of pointed sets
- category of pointed topological spaces
- category of pseudo-metric spaces with non-expansive maps
- category of sets and relations
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- simplex category
- walking commutative square
- walking coreflexive pair