Implication details
Claim: If a category is accessible and is infinitary coextensive, then it is trivial.
Proof: This follows from the dual implication.
This implication has a dual.
Show 66 categories using this implication
- empty category
- category of abelian groups
- category of finite sets and bijections
- delooping of the additive monoid of natural numbers
- category of Banach spaces with linear contractions
- 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 monoids
- 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 fields
- category of fields of characteristic zero
- category of finitely generated free abelian groups
- category of groups
- category of Jónsson-Tarski algebras
- category of M-sets
- category of extended metric spaces
- 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
- 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 rngs
- category of semigroups
- category of sequences of abelian groups
- category of sequences of sets
- category of sets
- category of pointed sets
- category of set functions and commutative squares
- category of non-empty sets
- category of pairs of sets
- category of sheaves
- category of abelian sheaves
- category of combinatorial species
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- category of finite Z-sets
- category of Z-sets
- forked commutative square
- category of graded abelian groups
- category of graded modules over a graded ring
- real interval [0,1]
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking coreflexive pair
- walking fork
- walking morphism
- walking parallel pair
- walking span