Implication details
Claim: If a category is one-way, then it is Cauchy complete and is core-thin.
Proof: This is trivial.
Show 71 categories using this implication
- empty category
- trivial category
- discrete category on two objects
- category of algebras
- 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 a reflexive binary relation
- category of sets equipped with a symmetric binary relation
- category of sets equipped with a symmetric reflexive binary relation
- category of commutative algebras
- category of commutative rings
- category of small categories
- category of coproducts of Euclidean spaces
- category of F(I)-sets
- category of finite sets and injections
- category of finite sets and surjections
- category of finite sets of even cardinality
- category of fields
- category of fields of characteristic zero
- category of finitely generated free modules over Z x Z
- category of Hausdorff spaces
- category of Jónsson-Tarski algebras
- category of locally ringed spaces
- category of M-sets
- category of measurable spaces
- category of extended metric spaces
- category of sets with a distinguished subset
- partially ordered set of natural numbers
- partially ordered set of extended natural numbers
- partially ordered collection of ordinal numbers
- category of partially ordered sets
- category of partially ordered sets without isolated points
- category of preordered sets
- category of quivers
- category of sets and relations
- category of rings
- category of rngs
- category of sequences of sets
- category of sets
- category of set functions and commutative squares
- category of sets and bijections
- category of countable sets
- discrete category of sets
- category of large families of sets
- category of large families of sets and bijections
- category of large families of sets which are mostly empty
- indiscrete category of sets
- category of non-empty sets
- category of pairs of sets
- category of sheaves
- category of topological spaces
- category of Z-functors
- category of Z-sets
- preordered set of integers w.r.t. divisibility
- cocompletion of a discrete–pair join
- forked commutative square
- category of ω-sets
- real interval [0,1]
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking fork
- walking idempotent
- walking isomorphism
- walking morphism
- walking parallel pair
- walking span