Implication Details
Claim: If a category is connected, then it is inhabited.
Proof: This holds by definition.
Show 46 categories using this implication
- empty category
- category of algebras
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of small categories
- category of cochain complexes of abelian groups
- simplex category
- category of finite sets and injections
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- category of finite sets
- category of locally ringed spaces
- category of smooth manifolds
- category of metric spaces with non-expansive maps
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- category of monoids
- partially ordered set of natural numbers
- partially ordered set of extended natural numbers
- partially ordered collection of ordinal numbers
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of preordered sets
- category of rings
- category of rngs
- category of schemes
- category of semigroups
- category of sequences of abelian groups
- category of sets
- category of set functions and commutative squares
- category of countable sets
- category of sets with finite-to-one maps
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of Z-functors
- preordered set of integers w.r.t. divisibility
- category of graded abelian groups
- category of graded modules over a graded ring
- real interval [0,1]
- walking commutative square
- walking composable pair
- walking coreflexive pair
- walking morphism
- walking parallel pair