category of simplicial sets
- notation:
- objects: simplicial sets, i.e. functors
- morphisms: natural transformations
- nLab Link
Satisfied Properties
Properties from the database
- has a generator
- is a Grothendieck topos
- is locally small
- is locally strongly finitely presentable
Deduced properties
- is locally essentially small
- has a generating set
- is inhabited
- is regular
- is finitely complete
- has equalizers
- has coreflexive equalizers
- has finite products
- has binary products
- has a terminal object
- is connected
- has pullbacks
- is Cauchy complete
- has finite powers
- has binary powers
- is locally finitely presentable
- is locally presentable
- is locally ℵ₁-presentable
- is cocomplete
- is complete
- has connected limits
- has products
- has countable products
- has wide pullbacks
- has cofiltered limits
- has sequential limits
- has powers
- has countable powers
- is well-copowered
- is well-powered
- has exact filtered colimits
- has filtered colimits
- has directed colimits
- has coproducts
- is an elementary topos
- is cartesian closed
- is infinitary distributive
- is distributive
- has finite coproducts
- has a strict initial object
- has an initial object
- has a subobject classifier
- is mono-regular
- is balanced
- has a regular subobject classifier
- has disjoint finite coproducts
- has disjoint coproducts
- is epi-regular
- is finitely cocomplete
- has a cogenerator
- is locally cartesian closed
- is coregular
- is extensive
- is lextensive
- is infinitary extensive
- is co-Malcev
- has connected colimits
- has sifted colimits
- has reflexive coequalizers
- has cosifted limits
- has countable coproducts
- has binary coproducts
- has coequalizers
- has sequential colimits
- has pushouts
- has directed limits
- has wide pushouts
- has copowers
- has countable copowers
- has finite copowers
- has binary copowers
- has a cogenerating set
Unsatisfied Properties
Properties from the database
- is not Malcev
- is not skeletal
- does not have a strict terminal object
Deduced properties*
- is not direct
- is not discrete
- is not thin
- is not left cancellative
- is not a groupoid
- is not one-way
- is not essentially discrete
- is not trivial
- is not pointed
- does not have zero morphisms
- does not have biproducts
- is not preadditive
- is not additive
- is not abelian
- is not Grothendieck abelian
- is not split abelian
- is not essentially small
- is not small
- is not finite
- is not essentially finite
- is not self-dual
- is not unital
- does not have disjoint finite products
- does not have disjoint products
- is not right cancellative
- is not codistributive
- is not infinitary codistributive
- is not coextensive
- is not infinitary coextensive
- is not inverse
- is not counital
*This also uses the deduced satisfied properties.
Unknown properties
There are 2 properties for which the database doesn't have an answer if they are satisfied or not. Please help to contribute the data!
Special objects
- terminal object: simplicial set with
- initial object: simplicial set with
- products: pointwise defined direct product
- coproducts: pointwise disjoint union
Special morphisms
- isomorphisms: natural isomorphisms
- monomorphisms: pointwise injective transformations
- epimorphisms: pointwise surjective transformations
- regular monomorphisms: same as monomorphisms
- regular epimorphisms: same as epimorphisms