Implication Details
Claim: If a category has a terminal object, then it is ℵ₁-filtered.
Proof: This is obvious.
Show 46 categories using this implication
- category of abelian groups
- category of finitely generated abelian groups
- category of algebras
- category of Banach spaces with linear contractions
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- simplex category
- category of coproducts of Euclidean spaces
- category of finite abelian groups
- category of finite 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 groups
- category of smooth manifolds
- category of metric spaces with non-expansive maps
- category of metric spaces with continuous maps
- category of monoids
- 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 rings
- category of rngs
- category of schemes
- category of pointed sets
- category of non-empty sets
- category of combinatorial species
- category of pointed topological spaces
- category of vector spaces
- preordered set of integers w.r.t. divisibility
- cocompletion of a discrete–pair join
- walking coreflexive pair
- walking span
- walking splitting