Implication details
Claim: If a category is finitely accessible, then it has filtered colimits.
Proof: This holds by definition.
This implication has a dual.
Show 69 categories using this implication
- category of abelian groups
- category of finitely generated abelian groups
- category of algebras
- delooping of the additive monoid of natural numbers
- category of sets equipped with a binary relation
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a reflexive binary relation
- category of sets equipped with a symmetric binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of sets equipped with a symmetric reflexive binary relation
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of small categories
- category of cochain complexes of abelian groups
- simplex category
- category of finite sets and injections
- category of finite sets and surjections
- 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 fields
- category of fields of characteristic zero
- category of finitely generated free abelian groups
- category of groups
- category of countable groups
- category of smooth manifolds
- category of monoids
- category of sets with a distinguished subset
- partially ordered set of natural numbers
- partially ordered set of extended natural numbers
- category of partially ordered sets
- category of preordered sets
- category of finitely generated projective modules over the ring of dual numbers
- category of quivers with finite components
- category of left modules over a ring
- category of left modules over a division ring
- category of left modules over a non-semisimple ring
- category of rings
- category of rngs
- category of schemes
- category of semigroups
- category of sequences of abelian groups
- category of connected sequences of sets
- category of pointed sets
- category of countable sets
- category of sets with finite-to-one maps
- category of non-empty sets
- category of empty-or-finite pairs of sets
- category of combinatorial species
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- category of countable-dimensional vector spaces
- category of finite Z-sets
- forked commutative square
- category of graded abelian groups
- category of graded modules over a graded ring
- walking commutative square
- walking composable pair
- walking fork
- walking morphism
- walking parallel pair