Implication Details
Claim: If a category is essentially small, then it has an extremal generating collection and is locally essentially small and is well-copowered and is well-powered.
Proof: This is trivial.
This implication has a dual.
Show 61 categories using this implication
- empty category
- discrete category on two objects
- category of large families of abelian groups
- category of finitely generated abelian groups
- category of finite sets and bijections
- 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
- simplex category
- category of finite sets and injections
- category of finite sets and surjections
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- category of finite sets
- category of finite sets of even cardinality
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- 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 finitely generated free abelian groups
- category of finitely generated free modules over Z x Z
- category of countable groups
- category of Hausdorff spaces
- category of smooth manifolds
- category of measurable spaces
- partially ordered set of natural numbers
- partially ordered set of extended natural numbers
- category of finitely generated projective modules over the ring of dual numbers
- category of schemes
- category of countable sets
- category of large families of sets
- category of large families of sets and bijections
- category of large families of sets which are mostly singletons
- category of combinatorial species
- category of topological spaces
- category of pointed topological spaces
- category of long transfinite sequences of abelian groups
- category of uniform spaces
- category of countable-dimensional vector spaces
- category of Z-functors
- category of finite Z-sets
- preordered set of integers w.r.t. divisibility
- cocompletion of a discrete–pair join
- forked commutative square
- 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