Implication Details
Claim: If a category is finitely complete, then it is cofiltered.
Proof: This follows from the dual implication.
This implication has a dual.
Show 87 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 algebras
- category of Banach spaces with linear contractions
- category of sets equipped with a binary relation
- category of sets equipped with a reflexive binary relation
- category of sets equipped with a symmetric binary relation
- category of sets equipped with a symmetric reflexive binary relation
- category of commutative algebras
- category of commutative rings
- category of small categories
- category of cochain complexes of abelian groups
- simplex category
- category of F(I)-sets
- category of filtered vector spaces
- category of finite abelian groups
- category of finite groups
- 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 groups
- category of countable groups
- category of Jónsson-Tarski algebras
- category of locally ringed spaces
- category of M-sets
- category of measurable spaces
- category of metric spaces with ∞ allowed
- category of monoids
- category of sets with a distinguished subset
- partially ordered set of extended natural numbers
- category of partially ordered sets
- category of preordered sets
- category of quivers
- category of quivers with finite components
- 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 rings
- category of rngs
- category of schemes
- category of sequences of abelian groups
- category of sequences of sets
- category of connected sequences of sets
- category of sets
- category of pointed 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
- indiscrete category of sets
- category of non-empty sets
- category of pairs of sets
- category of empty-or-finite pairs of sets
- category of sheaves
- category of abelian sheaves
- category of combinatorial species
- category of topological spaces
- 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 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
- category of finite Z-sets
- category of Z-sets
- preordered set of integers w.r.t. divisibility
- 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