Implication details
Claim: If a category has connected colimits, then it has sifted colimits.
Proof: This is because every sifted category is connected.
This implication has a dual.
Show 61 categories using this implication
- empty category
- trivial category
- discrete category on two objects
- category of large families of abelian groups
- category of finitely generated abelian groups
- category of Banach spaces with linear contractions
- category of sets equipped with a binary relation
- category of sets equipped with an irreflexive 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 irreflexive binary relation
- category of sets equipped with a symmetric reflexive binary relation
- category of small categories
- category of compact Hausdorff spaces
- category of F(I)-sets
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- category of finite sets
- 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 finitely generated free abelian groups
- category of countable groups
- category of finitely generated groups
- category of Hausdorff spaces
- category of locally ringed spaces
- category of measurable spaces
- category of extended metric spaces
- category of sets with a distinguished subset
- partially ordered set of natural numbers
- partially ordered collection of ordinal numbers
- category of partially ordered sets
- category of preordered sets
- category of connected sequences of sets
- category of countable sets
- discrete category of sets
- category of large families of sets
- category of large families of sets which are mostly empty
- category of large families of sets which are mostly singletons
- indiscrete category 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 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
- preordered set of integers w.r.t. divisibility
- cocompletion of a discrete–pair join
- category of ω-sets
- real interval [0,1]
- walking isomorphism