Implication details
Claim: If a category is essentially finite, then it is essentially countable and is locally finite.
Proof: This is trivial.
Show 42 categories using this implication
- empty category
- trivial category
- discrete category on two objects
- category of large families of abelian groups
- category of finitely generated abelian groups
- 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 finite-dimensional vector spaces [countable 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 finitely generated free modules over Z x Z
- category of finitely generated groups
- category of metric spaces with non-expansive maps
- category of pseudo-metric spaces with non-expansive maps
- category of finitely generated projective modules over the ring of dual numbers
- category of connected sequences of sets
- category of sets and bijections
- discrete category of sets
- category of large families of sets and bijections
- category of sets with finite-to-one maps
- indiscrete category of sets
- category of empty-or-finite pairs of sets
- category of combinatorial species
- category of Z-functors
- forked commutative square
- category of ω-sets
- real interval [0,1]
- walking commutative square
- walking composable pair
- walking coreflexive pair
- walking fork
- walking idempotent
- walking isomorphism
- walking morphism
- walking parallel pair
- walking span
- walking splitting