Implication Details
Claim: A category is connected and has a multi-initial object if and only if it has an initial object.
Proof: This follows from the dual implication.
Show 54 categories using this implication
- category of algebras
- category of Banach spaces with linear contractions
- category of combinatorial species
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of countable groups
- category of countable sets
- category of fields
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- category of finite sets
- category of finite sets and bijections
- category of finite sets and injections
- category of finite sets and surjections
- 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 groups
- category of metric spaces with continuous maps
- category of metric spaces with non-expansive maps
- category of monoids
- category of non-empty sets
- category of pointed sets
- category of pointed topological spaces
- category of pseudo-metric spaces with non-expansive maps
- category of rings
- category of rngs
- category of schemes
- category of semigroups
- category of sets and relations
- category of sets with a distinguished subset
- category of sets with finite-to-one maps
- category of smooth manifolds
- delooping of a non-trivial finite group
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- discrete category on two objects
- empty category
- partially ordered collection of ordinal numbers
- partially ordered set of extended natural numbers
- partially ordered set of natural numbers
- real interval [0,1]
- simplex category
- walking composable pair
- walking coreflexive pair
- walking fork
- walking idempotent
- walking morphism
- walking parallel pair
- walking splitting