Implication Details
Claim: If a category is essentially small, then it has an extremal cogenerating collection and is locally essentially small and is well-copowered and is well-powered.
Proof: This follows from the dual implication.
This implication has a dual.
Show 33 categories using this implication
- empty category
- discrete category on two objects
- category of finitely generated abelian groups
- category of finite sets and bijections
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of finite sets and injections
- category of finite abelian groups
- category of finite groups
- 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 countable groups
- 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 sets and bijections
- category of large families of sets which are mostly empty
- category of sets with finite-to-one maps
- category of combinatorial species
- category of countable-dimensional vector spaces
- category of finite Z-sets
- preordered set of integers w.r.t. divisibility
- forked commutative square
- real interval [0,1]
- walking commutative square
- walking composable pair
- walking fork
- walking isomorphism
- walking morphism