Implication Details
Claim: If a category has pullbacks, then it has kernel pairs.
Proof: This is trivial.
This implication has a dual.
Show 58 categories using this implication
- empty category
- trivial category
- discrete category on two objects
- category of large families of abelian groups
- 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 F(I)-sets
- category of finite sets and surjections
- category of finite sets
- category of Hausdorff spaces
- category of Jónsson-Tarski algebras
- category of locally ringed spaces
- category of M-sets
- category of smooth manifolds
- category of measurable spaces
- category of metric spaces with non-expansive maps
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- category of sets with a distinguished subset
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of preordered sets
- category of rings
- category of schemes
- category of sets
- category of sets and bijections
- 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
- category of large families of sets which are mostly singletons
- category of sets with finite-to-one maps
- indiscrete category of sets
- category of sheaves
- category of combinatorial species
- category of topological spaces
- category of pointed topological spaces
- category of torsion abelian groups
- category of long transfinite sequences of abelian groups
- category of uniform spaces
- category of large families of vector spaces which are mostly zero
- category of finite Z-sets
- category of Z-sets
- real interval [0,1]
- walking commutative square
- walking isomorphism
- walking span