dual of the category of sets
- notation:
- objects: sets
- morphisms: A morphism is a map of sets .
- nLab Link
- Dual category:
By definition, this category is the dual (or opposite) of the category of sets.
Satisfied Properties
Properties from the database
—
Deduced properties
- is balanced
- has binary coproducts
- has binary products
- is Cauchy complete
- is cocomplete
- is codistributive
- has coequalizers
- is coextensive
- has cofiltered limits
- has a cogenerating set
- has a cogenerator
- is complete
- is connected
- has connected colimits
- has connected limits
- has coproducts
- is coregular
- has countable coproducts
- has countable products
- has directed colimits
- has directed limits
- has disjoint finite products
- has disjoint products
- is epi-regular
- has equalizers
- has filtered colimits
- has finite coproducts
- has finite products
- is finitely cocomplete
- is finitely complete
- has a generating set
- has a generator
- is infinitary codistributive
- is infinitary coextensive
- is inhabited
- has an initial object
- is locally essentially small
- is locally small
- is Malcev
- is mono-regular
- has products
- has pullbacks
- has pushouts
- is regular
- has sequential colimits
- has sequential limits
- has a strict terminal object
- is strongly connected
- has a terminal object
- is well-copowered
- is well-powered
- has wide pullbacks
- has wide pushouts
Unsatisfied Properties
Properties from the database
- is not locally presentable
Deduced properties*
- is not abelian
- is not additive
- does not have biproducts
- is not co-Malcev
- is not counital
- is not discrete
- does not have disjoint coproducts
- does not have disjoint finite coproducts
- is not distributive
- is not essentially discrete
- is not essentially finite
- is not essentially small
- is not extensive
- is not finite
- is not a groupoid
- is not infinitary distributive
- is not infinitary extensive
- is not left cancellative
- is not pointed
- is not preadditive
- is not right cancellative
- is not self-dual
- is not skeletal
- is not small
- is not split abelian
- does not have a strict initial object
- is not thin
- is not trivial
- is not unital
- does not have zero morphisms
- is not locally finitely presentable
- is not locally ℵ₁-presentable
- is not Grothendieck abelian
- is not locally strongly finitely presentable
- is not finitary algebraic
- is not a Grothendieck topos
*This also uses the deduced satisfied properties.
Unknown properties
There are 7 properties for which the database doesn't have an answer if they are satisfied or not. Please help to contribute the data!
Special objects
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Special morphisms
- isomorphisms:
- monomorphisms:
- epimorphisms:
- regular monomorphisms:
- regular epimorphisms: