Implication details
Claim: If a category is one-way, then it is retract-trivial.
Proof: This is trivial.
Show 69 categories using this implication
- empty category
- discrete category on two objects
- delooping of the bicyclic monoid
- delooping of the double bicyclic monoid
- category of Banach spaces with linear contractions
- 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 monoids
- category of small categories
- simplex category
- category of F(I)-sets
- category of finite groups
- category of finite ordered sets
- 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 groups
- category of countable groups
- category of Hausdorff spaces
- category of Jónsson-Tarski algebras
- category of locally ringed spaces
- category of M-sets
- category of measurable spaces
- category of metric spaces with continuous maps
- 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
- partially ordered collection of ordinal 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 rngs
- category of schemes
- category of sequences of sets
- category of sets
- category of pointed sets
- category of set functions and commutative squares
- category of countable sets
- discrete category of sets
- category of large families of sets
- category of large families of sets which are mostly empty
- category of sets with finite-to-one maps
- category of pairs of sets
- category of sheaves
- category of topological spaces
- category of pointed topological spaces
- category of large families of vector spaces which are mostly zero
- category of Z-functors
- category of Z-sets
- preordered set of integers w.r.t. divisibility
- cocompletion of a discrete–pair join
- category of ω-sets
- 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
- walking splitting