Implication Details
Assumptions: cofiltered limits, extensive, terminal object
Conclusions: cocartesian cofiltered limits
Proof: Let be an extensive category with cofiltered limits and a terminal object. Then the coproduct functor is an equivalence. The forgetful functor creates connected limits, and hence preserves cofiltered limits. For every the functor also preserves cofiltered limits. The composition of these functors is and therefore also preserves cofiltered limits.
Show 22 categories using this implication
- category of algebras
- category of small categories
- category of compact Hausdorff spaces
- 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 monoids
- category of posets
- category of prosets
- category of rings
- category of rngs
- category of sets
- category of pairs of sets
- category of sheaves
- category of topological spaces
- category of Z-functors
- proset of integers w.r.t. divisibility
- category of simplicial sets