Implication Details
Claim: If a category has an initial object, then it is ℵ₁-cofiltered.
Proof: This follows from the dual implication.
Show 72 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
- category of small categories
- category of coproducts of Euclidean spaces
- category of finite sets and injections
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- category of finite sets
- category of finite sets of even cardinality
- 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 fields of characteristic zero
- 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 countable groups
- category of Jónsson-Tarski algebras
- category of M-sets
- category of smooth manifolds
- category of metric spaces with non-expansive maps
- category of metric spaces with ∞ allowed
- category of monoids
- partially ordered set of natural numbers
- partially ordered collection of ordinal numbers
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of partially ordered sets without isolated points
- 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 sets and relations
- category of rings
- category of rngs
- category of schemes
- category of semigroups
- category of sets
- category of pointed sets
- category of set functions and commutative squares
- category of countable sets
- category of sets with finite-to-one maps
- category of non-empty sets
- category of pairs of sets
- category of sheaves
- category of abelian sheaves
- category of combinatorial species
- category of pointed topological spaces
- category of uniform spaces
- category of vector spaces
- category of countable-dimensional vector spaces
- category of large vector spaces over a large field with a small basis
- preordered set of integers w.r.t. divisibility
- cocompletion of a discrete–pair join
- forked commutative square
- real interval [0,1]
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking fork
- walking morphism
- walking span
- walking splitting