category of combinatorial species
- notation:
- objects: combinatorial species, defined as functors , where is the category of finite sets and bijections
- morphisms: natural transformations
- nLab Link
- Related categories: ,
Most categorical properties are immediately inferred from . Notice that this category is not locally small; it is just equivalent to a locally small category.
Properties
Properties from the database
- has disjoint finite coproducts
- is distributive
- is epi-regular
- is essentially small
- is finitely cocomplete
- is finitely complete
- is mono-regular
Deduced properties
- is locally essentially small
- is well-copowered
- is well-powered
- has equalizers
- has finite products
- has binary products
- has a terminal object
- has pullbacks
- is connected
- has finite coproducts
- is Cauchy complete
- has a strict initial object
- has an initial object
- is inhabited
- is balanced
- has coequalizers
- has binary coproducts
- has pushouts
Non-Properties
Non-Properties from the database
- is not Malcev
- does not have countable coproducts
- does not have countable products
- is not locally small
- is not skeletal
- does not have a strict terminal object
Deduced Non-Properties*
- is not small
- is not finite
- is not discrete
- does not have products
- is not complete
- does not have filtered limits
- does not have wide pullbacks
- does not have connected limits
- is not essentially discrete
- is not trivial
- is not thin
- is not essentially finite
- is not left cancellative
- is not pointed
- does not have zero morphisms
- does not have sequential limits
- is not locally presentable
- is not locally finitely presentable
- is not locally ℵ₁-presentable
- is not finitary algebraic
- is not a Grothendieck topos
- is not preadditive
- is not additive
- is not abelian
- is not Grothendieck abelian
- is not split abelian
- is not a groupoid
- does not have coproducts
- does not have disjoint coproducts
- is not infinitary distributive
- is not right cancellative
- is not cocomplete
- does not have filtered colimits
- does not have exact filtered colimits
- does not have wide pushouts
- does not have connected colimits
- does not have sequential colimits
- is not self-dual
*This also uses the deduced properties.
Unknown properties
For these properties the database currently doesn't have an answer if they are satisfied or not. Please help to complete the data!
- is cartesian closed
- has a cogenerator
- is an elementary topos
- has a generator
- has a subobject classifier
Special morphisms
- Isomorphisms: natural isomorphisms
- Monomorphisms: pointwise injective natural transformations
- Epimorphisms: pointwise surjective natural transformations