Implication Details
Claim: If a category has a strict initial object, then it has an initial object.
Proof: This holds by definition.
This implication has a dual.
Show 38 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 small categories
- category of compact Hausdorff spaces
- simplex category
- category of coproducts of Euclidean spaces
- category of finite sets and surjections
- category of finite ordered sets
- category of finite sets of even cardinality
- category of fields
- 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 pseudo-metric spaces with non-expansive maps
- category of partially ordered sets without isolated points
- category of quivers with finite components
- category of schemes
- category of semigroups
- 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 singletons
- category of empty-or-finite pairs of sets
- category of uniform spaces
- preordered set of integers w.r.t. divisibility
- forked commutative square
- walking coreflexive pair
- walking idempotent
- walking parallel pair