Implication details
Claim: If a category has sifted colimits, then it has filtered colimits and has reflexive coequalizers.
Proof: This is because filtered categories are sifted and because the index category for a reflexive coequalizer is sifted.
This implication has a dual.
Show 70 categories using this implication
- category of finitely generated abelian groups
- category of algebras
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of compact Hausdorff spaces
- simplex category
- 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 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 countable groups
- category of finitely generated groups
- category of Hausdorff spaces
- category of Jónsson-Tarski algebras
- category of locally ringed spaces
- category of M-sets
- category of smooth manifolds
- category of metric spaces with continuous maps
- category of monoids
- partially ordered set of natural numbers
- partially ordered collection of ordinal numbers
- category of partially ordered sets without isolated points
- category of finitely generated projective modules over the ring of dual numbers
- category of quivers
- category of quivers with finite components
- category of sets and relations
- category of rings
- category of rngs
- category of schemes
- category of semigroups
- category of sequences of sets
- category of connected sequences of sets
- category of sets
- category of set functions and commutative squares
- category of countable sets
- category of large families of sets which are mostly singletons
- category of sets with finite-to-one maps
- category of non-empty sets
- category of pairs of sets
- category of empty-or-finite pairs of sets
- category of combinatorial species
- category of countable-dimensional vector spaces
- category of finite Z-sets
- category of Z-sets
- preordered set of integers w.r.t. divisibility
- category of ω-sets
- real interval [0,1]
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking idempotent
- walking morphism
- walking splitting