Implication details
Claim: If a category has a strict initial object, then it has a conatural numbers object.
Proof: This follows from the dual implication.
This implication has a dual.
Show 50 categories using this implication
- category of sets equipped with a binary relation
- category of sets equipped with an irreflexive 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 irreflexive binary relation
- category of sets equipped with a symmetric reflexive binary relation
- category of small categories
- category of compact Hausdorff spaces
- category of coproducts of Euclidean spaces
- category of finite sets and injections
- category of finite ordered sets
- category of finite sets
- category of finite sets of even cardinality
- category of fields of characteristic zero
- category of locally ringed spaces
- 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 extended metric spaces
- category of sets with a distinguished subset
- partially ordered set of natural numbers
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of partially ordered sets without isolated points
- category of preordered sets
- category of quivers
- category of quivers with finite components
- category of schemes
- category of semigroups
- category of sequences of sets
- category of set functions and commutative squares
- category of countable 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 empty-or-finite pairs of sets
- category of combinatorial species
- category of topological spaces
- category of uniform spaces
- category of Z-functors
- category of finite Z-sets
- preordered set of integers w.r.t. divisibility
- cocompletion of a discrete–pair join
- forked commutative square
- category of ω-sets
- category of simplicial sets
- walking commutative square
- walking fork
- walking span