Implication Details
Claim: If a category is preadditive, then it is locally essentially small and has zero morphisms.
Proof: This is trivial.
Show 41 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 fields
- category of free abelian groups
- 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 set functions and commutative squares
- 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 Z-functors
- preordered set of integers w.r.t. divisibility
- 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