Implication details
Claim: If a category has a conatural numbers object, then it has an initial object.
Proof: This follows from the dual implication.
This implication has a dual.
Show 26 categories using this implication
- empty category
- discrete category on two objects
- category of finite sets and bijections
- delooping of the bicyclic monoid
- delooping of the double bicyclic monoid
- 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
- simplex category
- category of finite sets and surjections
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- category of fields
- category of connected sequences of sets
- category of sets and bijections
- category of countably infinite sets
- discrete category of sets
- category of large families of sets and bijections
- category of large families of sets which are mostly singletons
- category of non-empty sets
- walking coreflexive pair
- walking idempotent
- walking parallel pair