Implication Details
Assumptions: locally finitely multi-presentable
Conclusions: filtered-colimit-stable monomorphisms
Proof: Every locally finitely multi-presentable category is a multi-reflective full subcategory of a presheaf category closed under filtered colimits (Adamek-Rosicky, 4.30). Since multi-reflective full subcategories are in general closed under connected limits (Adamek-Rosicky, Thm. 4.26), in particular, we can calculate not only filtered colimits but also kernel pairs as well as in a presheaf category.
Show 28 categories using this implication
- category of abelian groups
- category of algebras
- category of Banach spaces with linear contractions
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of compact Hausdorff spaces
- category of fields
- category of groups
- category of Hausdorff spaces
- category of metric spaces with non-expansive maps
- category of metric spaces with ∞ allowed
- category of monoids
- poset of extended natural numbers
- category of left modules over a ring
- category of left modules over a division ring
- category of rings
- category of rngs
- category of semigroups
- dual of the category of sets
- category of pointed sets
- dual of the category of topological spaces
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- walking commutative square
- walking composable pair
- walking morphism