Implication Details
Claim: If a category has binary products and has equalizers, then it has pullbacks.
Proof: The pullback of and is the equalizer of .
This implication has a dual.
Show 47 categories using this implication
- category of abelian groups
- category of finitely generated abelian groups
- category of algebras
- category of Banach spaces with linear contractions
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of small categories
- category of F(I)-sets
- category of filtered vector spaces
- category of finite abelian groups
- category of finite groups
- 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 free abelian groups
- category of finitely generated free abelian groups
- category of groups
- category of countable groups
- category of smooth manifolds
- category of metric spaces with non-expansive maps
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- category of monoids
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of preordered sets
- category of quivers with finite components
- 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 rings
- category of rngs
- category of semigroups
- category of connected sequences of sets
- category of pointed sets
- category of countable sets
- category of large families of sets
- category of empty-or-finite pairs of sets
- category of abelian sheaves
- category of vector spaces
- category of countable-dimensional vector spaces
- category of large vector spaces over a large field with a small basis
- preordered set of integers w.r.t. divisibility
- walking composable pair
- walking morphism