CatDat

Satisfied Properties

Assigned properties

• is small
• is finite
• is skeletal
• is self-dual
• is semi-strongly connected
• is finitary algebraic

Deduced properties

• is locally strongly finitely presentable
• is well-copowered
• is connected
• has a generator
• is essentially small
• is locally small
• is countable
• is essentially finite
• is locally finitely presentable
• is cocomplete
• is a generalized variety
• is regular
• is multi-algebraic
• is inhabited
• has a generating set
• is locally essentially small
• is well-powered
• is essentially countable
• is locally finite
• has a cogenerating set
• has a cogenerator
• is finitely accessible
• has exact filtered colimits
• is locally ℵ₁-presentable
• has sifted colimits
• is ℵ₁-accessible
• is locally finitely multi-presentable
• is multi-cocomplete
• has effective congruences
• is finitely complete
• has connected colimits
• is finitely cocomplete
• has coequalizers
• has coproducts
• is complete
• is coregular
• is locally presentable
• is accessible
• has ℵ₁-filtered colimits
• has filtered colimits
• has connected limits
• has filtered-colimit-stable monomorphisms
• has equalizers
• has products
• has finite products
• is multi-complete
• has quotients of congruences
• is Barr-exact
• has cartesian filtered colimits
• is filtered
• has reflexive coequalizers
• has finite coproducts
• has a multi-initial object
• is Cauchy complete
• is cofiltered
• has copowers
• has ℵ₂-small coproducts
• has wide pushouts
• has effective cocongruences
• has exact cofiltered limits
• has cosifted limits
• is locally multi-presentable
• has a multi-terminal object
• has coreflexive equalizers
• is sifted
• has directed colimits
• has powers
• has ℵ₂-small products
• has binary products
• has a terminal object
• has finite powers
• has wide pullbacks
• is coaccessible
• has an initial object
• has coquotients of cocongruences
• is Barr-coexact
• has cofiltered limits
• has cofiltered-limit-stable epimorphisms
• has cocartesian cofiltered limits
• is cosifted
• has countable coproducts
• has ℵ₂-small copowers
• has binary coproducts
• has finite copowers
• has pushouts
• is thin
• has ℵ₁-cofiltered limits
• is locally copresentable
• is Malcev
• has a natural numbers object
• is locally poly-presentable
• is locally cartesian closed
• is ℵ₁-filtered
• has countable products
• has ℵ₂-small powers
• has binary powers
• has pullbacks
• is left cancellative
• is one-way
• is co-Malcev
• is locally cocartesian coclosed
• is ℵ₁-cofiltered
• has directed limits
• has sequential colimits
• has countable copowers
• has binary copowers
• is right cancellative
• is cartesian closed
• has sequential limits
• has a strict initial object
• has countable powers
• has a regular subobject classifier
• is direct
• is core-thin
• is cocartesian coclosed
• has a strict terminal object
• has a regular quotient object classifier
• is inverse
• is distributive
• is countably distributive
• is infinitary distributive
• is gaunt
• is codistributive
• is countably codistributive
• is infinitary codistributive

Unsatisfied Properties

Assigned properties

• is not trivial

Deduced properties*

• is not pointed
• is not Grothendieck abelian
• is not strongly connected
• is not essentially discrete
• does not have disjoint finite coproducts
• is not additive
• does not have zero morphisms
• is not an elementary topos
• does not have disjoint finite products
• is not unital
• is not preadditive
• is not abelian
• does not have biproducts
• is not discrete
• is not a groupoid
• does not have disjoint coproducts
• does not have kernels
• does not satisfy CIP
• is not extensive
• is not normal
• does not have a subobject classifier
• is not a Grothendieck topos
• is not counital
• does not have disjoint products
• does not have cokernels
• does not satisfy CSP
• is not coextensive
• is not conormal
• is not split abelian
• is not infinitary extensive
• is not balanced
• is not mono-regular
• is not a pretopos
• is not infinitary coextensive
• does not have a quotient object classifier
• is not subobject-trivial
• is not epi-regular
• is not quotient-trivial

*This also uses the deduced satisfied properties.