Implication Details
Claim: If a category has cartesian filtered colimits, then it has filtered colimits and has finite products.
Proof: This holds by definition.
Show 40 categories using this implication
- category of Banach spaces with linear contractions
- category of combinatorial species
- category of countable groups
- category of countable sets
- category of fields
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- category of finite sets
- category of finite sets and bijections
- category of finite sets and injections
- category of finite sets and surjections
- 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 finitely generated abelian groups
- category of free abelian groups
- category of metric spaces with continuous maps
- category of metric spaces with non-expansive maps
- category of metric spaces with ∞ allowed
- category of schemes
- category of sets and relations
- category of sets with finite-to-one maps
- category of smooth manifolds
- delooping of a non-trivial finite group
- delooping of an infinite countable group
- delooping of an infinite uncountable group
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- discrete category on two objects
- empty category
- partially ordered collection of ordinal numbers
- partially ordered set of natural numbers
- simplex category
- walking coreflexive pair
- walking fork
- walking idempotent
- walking parallel pair
- walking span
- walking splitting