Implication Details
Claim: If a category is finitely cocomplete, then it is filtered.
Proof: Every finite diagram even admits a universal cocone.
Show 55 categories using this implication
- category of abelian groups
- category of abelian sheaves
- category of Banach spaces with linear contractions
- category of combinatorial species
- category of compact Hausdorff spaces
- category of countable sets
- category of fields
- category of filtered vector spaces
- category of finite abelian groups
- category of finite sets
- category of finite sets and bijections
- category of finite sets and surjections
- 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 abelian groups
- category of Hausdorff spaces
- category of Jónsson-Tarski algebras
- category of left modules over a division ring
- category of left modules over a ring
- category of locally ringed spaces
- category of M-sets
- category of measurable spaces
- category of metric spaces with ∞ allowed
- category of pairs of sets
- category of partially ordered sets
- category of pointed sets
- category of pointed topological spaces
- category of preordered sets
- category of semigroups
- category of set functions and commutative squares
- category of sets
- category of sets with a distinguished subset
- category of sets with finite-to-one maps
- category of sheaves
- category of simplicial sets
- category of small categories
- category of topological spaces
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- category of Z-functors
- discrete category on two objects
- empty category
- partially ordered collection of ordinal numbers
- partially ordered set of extended natural numbers
- partially ordered set of natural numbers
- preordered set of integers w.r.t. divisibility
- real interval [0,1]
- trivial category
- walking commutative square
- walking composable pair
- walking isomorphism
- walking morphism
- walking span