Implication Details
Claim: If a category is locally cocartesian coclosed and has a terminal object, then it has a strict terminal object.
Proof: This follows from the dual implication.
This implication has a dual.
Show 69 categories using this implication
- trivial category
- category of abelian groups
- category of large families of abelian groups
- category of finitely generated abelian groups
- category of Banach spaces with linear contractions
- category of sets with a binary relation
- category of cochain complexes of abelian groups
- category of compact Hausdorff spaces
- simplex category
- category of directed graphs
- 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 finitely generated free abelian groups
- category of Jónsson-Tarski algebras
- category of locally ringed spaces
- category of M-sets
- category of measurable spaces
- category of metric spaces with non-expansive maps
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- category of sets with a distinguished subset
- partially ordered set of extended natural numbers
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of preordered sets
- 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 sequences of abelian groups
- category of sets
- category of set functions and commutative squares
- category of countable sets
- category of large families of sets
- category of large families of sets which are mostly singletons
- category of non-empty sets
- category of pairs of sets
- category of sheaves
- category of abelian sheaves
- category of combinatorial species
- category of topological spaces
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of long transfinite sequences of abelian groups
- category of uniform spaces
- category of vector spaces
- 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
- category of Z-functors
- cocompletion of a discrete–pair join
- category of graded abelian groups
- category of graded modules over a graded ring
- real interval [0,1]
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking coreflexive pair
- walking isomorphism
- walking morphism
- walking splitting