Implication Details
Claim: If a category is core-connected and has an initial object, then it is trivial.
Proof: Every object is isomorphic to the initial object.
Show 39 categories using this implication
- category of abelian groups
- category of abelian sheaves
- category of Banach spaces with linear contractions
- category of compact Hausdorff spaces
- category of countable sets
- category of filtered vector spaces
- category of finite ordered sets
- category of finite-dimensional vector spaces [countable field]
- category of finite-dimensional vector spaces [finite field]
- category of finite-dimensional vector spaces [uncountable field]
- category of finitely generated abelian groups
- category of free abelian groups
- category of left modules over a division ring
- category of left modules over a ring
- category of M-sets
- category of metric spaces with continuous maps
- category of metric spaces with non-expansive maps
- category of metric spaces with ∞ allowed
- category of partially ordered sets
- category of pointed sets
- category of preordered sets
- category of pseudo-metric spaces with non-expansive maps
- category of sets
- category of sets and relations
- category of simplicial sets
- category of small categories
- category of smooth manifolds
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- 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
- partially ordered collection of ordinal numbers
- walking idempotent
- walking morphism
- walking splitting