category of finite sets and injections
This category is badly-behaved in itself, but plays an important role in representation theory.
Properties
Properties from the database
- has connected limits
- is epi-regular
- is essentially small
- has a generator
- has an initial object
- is left cancellative
- is locally small
- is mono-regular
Deduced properties
- is locally essentially small
- is well-copowered
- is well-powered
- has equalizers
- has wide pullbacks
- has filtered limits
- has pullbacks
- has a strict initial object
- is Cauchy complete
- has sequential limits
- is inhabited
- is balanced
- is connected
Non-Properties
Non-Properties from the database
- does not have binary coproducts
- does not have binary products
- does not have a cogenerator
- is not essentially finite
- does not have sequential colimits
- is not skeletal
- is not small
Deduced Non-Properties*
- is not finite
- is not discrete
- is not trivial
- is not essentially discrete
- does not have finite products
- is not finitely complete
- is not complete
- does not have products
- does not have a terminal object
- is not pointed
- does not have zero morphisms
- does not have countable products
- does not have exact filtered colimits
- is not infinitary distributive
- is not distributive
- is not locally presentable
- is not locally finitely presentable
- is not locally ℵ₁-presentable
- is not finitary algebraic
- is not an elementary topos
- is not cartesian closed
- is not a Grothendieck topos
- does not have a subobject classifier
- is not preadditive
- is not additive
- is not abelian
- is not Grothendieck abelian
- is not split abelian
- is not a groupoid
- is not right cancellative
- is not Malcev
- is not thin
- does not have coequalizers
- does not have coproducts
- does not have disjoint coproducts
- is not cocomplete
- is not finitely cocomplete
- does not have finite coproducts
- does not have disjoint finite coproducts
- does not have pushouts
- does not have connected colimits
- does not have wide pushouts
- does not have a strict terminal object
- does not have countable coproducts
- does not have filtered colimits
- is not self-dual
*This also uses the deduced properties.
Unknown properties
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Special morphisms
- Isomorphisms: bijective maps
- Monomorphisms: every morphism
- Epimorphisms: bijective maps