Implication Details
Assumptions: strict initial object
Conclusions: initial object
Proof: This holds by definition.
Show 43 categories using this implication
- category of compact Hausdorff spaces
- category of countable sets
- category of fields
- category of finite ordered sets
- category of finite sets and bijections
- category of finite sets and surjections
- category of Hausdorff spaces
- category of Jónsson-Tarski algebras
- category of locally ringed spaces
- category of M-sets
- category of measurable spaces
- category of metric spaces with continuous maps
- category of metric spaces with non-expansive maps
- category of metric spaces with ∞ allowed
- category of non-empty sets
- category of pairs of sets
- category of posets
- category of prosets
- category of pseudo-metric spaces with non-expansive maps
- category of schemes
- category of semigroups
- category of sets
- category of sets with finite-to-one maps
- category of sheaves
- category of simplicial sets
- category of small categories
- category of smooth manifolds
- category of topological spaces
- category of Z-functors
- delooping of a non-trivial finite group
- delooping of an infinite countable group
- delooping of an infinite uncountable group
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- discrete category on two objects
- empty category
- proset of integers w.r.t. divisibility
- simplex category
- trivial category
- walking coreflexive pair
- walking idempotent
- walking isomorphism
- walking parallel pair