Implication Details
Claim: If a category has countable products and has equalizers, then it has sequential limits.
Proof: See Mac Lane, V.2, Prop. 3. The proof can easily be adapted to this case. Namely, the limit of is the equalizer of two suitable endomorphisms of .
This implication has a dual.
Show 46 categories using this implication
- category of large families of abelian groups
- 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 small categories
- category of cochain complexes of abelian groups
- category of F(I)-sets
- category of filtered vector spaces
- category of finite ordered sets
- 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 continuous maps
- category of metric spaces with ∞ allowed
- category of sets with a distinguished subset
- category of partially ordered sets
- category of preordered sets
- category of quivers
- category of sequences of abelian groups
- category of sequences of sets
- category of sets
- category of set functions and commutative squares
- category of large families of 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 sheaves
- category of abelian sheaves
- category of 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 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]
- category of simplicial sets