Implication Details
Claim: If a category is complete, then it has connected limits and is finitely complete.
Proof: This is trivial.
This implication has a dual.
Show 52 categories using this implication
- empty category
- discrete category on two objects
- category of large families of abelian groups
- delooping of the additive monoid of ordinal numbers
- 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 cochain complexes of abelian groups
- category of compact Hausdorff spaces
- category of F(I)-sets
- category of finite sets and injections
- category of filtered vector spaces
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- category of fields of characteristic zero
- category of groups
- category of Hausdorff spaces
- 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 sets with a distinguished subset
- partially ordered collection of ordinal numbers
- category of sequences of abelian groups
- category of connected sequences of sets
- category of sets
- category of countable 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
- category of non-empty sets
- category of sheaves
- category of abelian sheaves
- 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 Z-functors
- 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]
- walking fork
- walking parallel pair