Implication details
Claim: If a category is countably coextensive and has filtered-colimit-stable monomorphisms, then it is thin.
Proof: This follows from the dual implication.
This implication has a dual.
Show 56 categories using this implication
- category of abelian groups
- category of large families of 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
- 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
- category of F(I)-sets
- category of finite sets and surjections
- category of filtered vector spaces
- category of fields
- category of fields of characteristic zero
- category of groups
- category of monoids
- category of partially ordered sets
- category of preordered sets
- 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 set functions and commutative squares
- category of sets and bijections
- category of large families of sets
- category of large families of sets and bijections
- category of large families of sets which are mostly empty
- category of non-empty sets
- category of pairs of sets
- category of sheaves
- category of abelian sheaves
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of long transfinite sequences of abelian groups
- category of uniform spaces
- category of vector spaces
- category of large families of vector spaces which are mostly zero
- cocompletion of a discrete–pair join
- forked commutative square
- category of graded abelian groups
- category of graded modules over a graded ring
- walking coreflexive pair
- walking fork
- walking parallel pair
- walking splitting