Implication Details
Claim: If a category is distributive, then it has finite coproducts and has finite products.
Proof: This holds by definition.
This implication has a dual.
Show 43 categories using this implication
- empty category
- discrete category on two objects
- 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
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- simplex category
- category of finite sets and injections
- category of finite sets and surjections
- category of finite groups
- category of finite ordered sets
- category of finite sets of even cardinality
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- category of fields
- category of fields of characteristic zero
- category of metric spaces with non-expansive maps
- partially ordered set of natural numbers
- partially ordered collection of ordinal numbers
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets without isolated points
- category of connected sequences of sets
- category of sets and bijections
- discrete category 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
- category of empty-or-finite pairs of sets
- preordered set of integers w.r.t. divisibility
- cocompletion of a discrete–pair join
- forked commutative square
- walking coreflexive pair
- walking fork
- walking idempotent
- walking parallel pair
- walking span
- walking splitting