Implication Details
Claim: A category is finitely cocomplete if and only if it has coequalizers and has finite coproducts.
Proof: This follows from the dual implication.
Show 58 categories using this implication
- category of finitely generated abelian groups
- category of algebras
- delooping of a group
- delooping of an infinite countable group
- delooping of a non-trivial finite group
- delooping of an infinite uncountable group
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- category of commutative algebras
- category of commutative rings
- simplex category
- category of finite sets and injections
- category of filtered vector spaces
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- category of finite sets
- category of finite-dimensional vector spaces
- category of finite-dimensional vector spaces [countable field]
- category of finite-dimensional vector spaces [finite field]
- category of finite-dimensional vector spaces [uncountable field]
- category of free abelian groups
- category of groups
- category of countable groups
- category of Hausdorff spaces
- category of locally ringed spaces
- category of smooth manifolds
- category of metric spaces with non-expansive maps
- category of metric spaces with continuous maps
- category of monoids
- partially ordered set of natural numbers
- partially ordered set of extended natural numbers
- partially ordered collection of ordinal numbers
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of preordered sets
- category of sets and relations
- category of rings
- category of rngs
- category of schemes
- category of pointed sets
- category of countable sets
- category of non-empty sets
- category of combinatorial species
- category of topological spaces
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of Z-functors
- forked commutative square
- real interval [0,1]
- walking commutative square
- walking composable pair
- walking coreflexive pair
- walking fork
- walking idempotent
- walking morphism
- walking parallel pair
- walking splitting