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 47 categories using this implication
- trivial category
- category of abelian groups
- category of finitely generated abelian groups
- category of Banach spaces with linear contractions
- category of commutative monoids
- category of cochain complexes of abelian groups
- simplex category
- category of coproducts of Euclidean spaces
- category of filtered vector spaces
- category of finite abelian groups
- category of finite ordered sets
- category of finite sets
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- 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 free abelian groups
- category of finitely generated free abelian groups
- category of finitely generated free modules over Z x Z
- category of countable groups
- category of metric spaces with non-expansive maps
- category of pseudo-metric spaces with non-expansive maps
- category of finitely generated projective modules over the ring of dual numbers
- category of left modules over a ring
- category of left modules over a division ring
- category of left modules over a non-semisimple ring
- category of sets and relations
- category of sequences of abelian groups
- category of pointed sets
- category of set-indexed families of abelian groups
- category of non-empty sets
- category of abelian sheaves
- category of combinatorial species
- category of pointed topological spaces
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of long transfinite sequences of abelian groups
- category of vector spaces
- category of countable-dimensional vector spaces
- category of large vector spaces over a large field with a small basis
- category of graded abelian groups
- category of graded modules over a graded ring
- walking commutative square
- walking coreflexive pair
- walking isomorphism