Implication Details
Claim: If a category is preadditive, then it has zero morphisms.
Proof: This is trivial.
Show 53 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
- simplex category
- category of finite sets and injections
- category of finite sets and surjections
- category of filtered vector spaces
- category of finite ordered sets
- category of finite sets
- category of finite sets of even cardinality
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- category of fields
- category of fields of characteristic zero
- category of free abelian groups
- category of finitely generated free abelian groups
- category of finitely generated free modules over Z x Z
- category of Jónsson-Tarski algebras
- category of sets with a distinguished subset
- partially ordered set of natural numbers
- partially ordered set of extended natural numbers
- category of partially ordered sets without isolated points
- category of finitely generated projective modules over the ring of dual numbers
- category of set functions and commutative squares
- discrete category of sets
- category of set-indexed families of abelian groups
- category of sets with finite-to-one maps
- category of pairs of sets
- category of sheaves
- category of combinatorial species
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of long transfinite sequences of abelian groups
- category of large vector spaces over a large field with a small basis
- preordered set of integers w.r.t. divisibility
- cocompletion of a discrete–pair join
- forked commutative square
- real interval [0,1]
- walking commutative square
- walking composable pair
- walking coreflexive pair
- walking fork
- walking idempotent
- walking morphism
- walking parallel pair
- walking span
- walking splitting