Implication Details
Assumptions: countable products, equalizers
Conclusions: sequential limits
Reason: 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 .
Show 27 categories using this implication
- category of small categories
- category of compact Hausdorff spaces
- category of finite ordered sets
- 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 posets
- category of prosets
- category of sets
- 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 Z-functors
- proset of integers w.r.t. divisibility
- poset [0,1]
- category of simplicial sets
- walking composable pair
- walking morphism