walking isomorphism

Satisfied properties

Assigned properties

• is small
• is finite
• is trivial

Deduced properties

• is core-connected
• is a Grothendieck topos
• is essentially discrete
• is essentially finite
• is one-sorted finitary algebraic
• is self-dual
• is split abelian
• is essentially small
• is locally small
• is countable
• is a Grothendieck cotopos
• is dually one-sorted finitary algebraic
• is abelian
• is finitary algebraic
• is well-copowered
• is strongly connected
• has an extremal generator
• is a groupoid
• is thin
• has connected limits
• is locally essentially small
• has an extremal generating collection
• is well-powered
• is essentially countable
• is locally finite
• is cartesian closed
• has exact filtered colimits
• is locally presentable
• has a subobject classifier
• is dually finitary algebraic
• has an extremal cogenerator
• has connected colimits
• has an extremal cogenerating collection
• is cocartesian coclosed
• has exact cofiltered limits
• is locally copresentable
• has a quotient object classifier
• is accessible
• is cocomplete
• is locally finitely presentable
• is complete
• is a generalized variety
• is additive
• has cokernels
• is conormal
• has kernels
• is normal
• has pullback-stable regular epimorphisms
• is finitely accessible
• is multi-algebraic
• has finite products
• is locally cartesian closed
• is semi-strongly connected
• has filtered colimits
• is finitely complete
• has filtered-colimit-stable monomorphisms
• has cartesian filtered colimits
• has sifted colimits
• has a generator
• has a generating collection
• has directed limits
• is left cancellative
• has equalizers
• has wide pullbacks
• is mono-regular
• has a regular subobject classifier
• is subobject-trivial
• is retract-trivial
• is one-way
• has binary powers
• is coaccessible
• is locally finitely copresentable
• is a dual generalized variety
• has pushout-stable regular monomorphisms
• is finitely coaccessible
• is dually multi-algebraic
• has finite coproducts
• is locally cocartesian coclosed
• has cofiltered limits
• is finitely cocomplete
• has cofiltered-limit-stable epimorphisms
• has cocartesian cofiltered limits
• has cosifted limits
• has a cogenerator
• has a cogenerating collection
• has directed colimits
• is right cancellative
• has coequalizers
• has wide pushouts
• is epi-regular
• has a regular quotient object classifier
• is quotient-trivial
• has binary copowers
• is Malcev
• has a parametrized natural numbers object
• is ℵ₁-accessible
• is Cauchy complete
• is locally multi-presentable
• is locally finitely multi-presentable
• is locally poly-presentable
• is preadditive
• has biproducts
• has effective congruences
• is multi-cocomplete
• has kernel pairs
• has pullbacks
• has products
• is multi-complete
• is connected
• has disjoint finite products
• is distributive
• has coreflexive equalizers
• has zero morphisms
• has a multi-initial object
• has a multi-terminal object
• is filtered
• has sequential limits
• has ℵ₁-filtered colimits
• has reflexive coequalizers
• is inhabited
• is balanced
• has binary products
• has a terminal object
• has finite powers
• is concretizable
• is regular-subobject-trivial
• is core-thin
• is an elementary topos
• is a quasitopos
• is total
• is co-Malcev
• has a coparametrized conatural numbers object
• is ℵ₁-coaccessible
• is locally multi-copresentable
• is locally finitely multi-copresentable
• is locally poly-copresentable
• has effective cocongruences
• has cokernel pairs
• has pushouts
• has coproducts
• has disjoint finite coproducts
• is codistributive
• is cofiltered
• has sequential colimits
• has ℵ₁-cofiltered limits
• has binary coproducts
• has an initial object
• has finite copowers
• is regular-quotient-trivial
• is an elementary cotopos
• is a quasicotopos
• is cototal
• is unital
• has a natural numbers object
• is locally ℵ₁-presentable
• is Grothendieck abelian
• has a strict initial object
• has quotients of congruences
• is pointed
• has disjoint coproducts
• is infinitary distributive
• satisfies CIP
• is extensive
• is sifted
• is ℵ₁-filtered
• has powers
• has ℵ₂-small products
• has countable products
• has countable powers
• has copowers
• is coregular
• is counital
• has a conatural numbers object
• is locally ℵ₁-copresentable
• is co-Grothendieck abelian
• has a strict terminal object
• has coquotients of cocongruences
• has disjoint products
• is infinitary codistributive
• satisfies CSP
• is coextensive
• is cosifted
• is ℵ₁-cofiltered
• has ℵ₂-small coproducts
• has countable coproducts
• has countable copowers
• is regular
• has coequalizers of kernel pairs
• is countably distributive
• is infinitary extensive
• is countably extensive
• has ℵ₂-small powers
• is Barr-exact
• has equalizers of cokernel pairs
• is countably codistributive
• is infinitary coextensive
• is countably coextensive
• has ℵ₂-small copowers
• is Barr-coexact
• is a pretopos
• is a precotopos

Unsatisfied properties

Assigned properties

• is not skeletal

Deduced properties*

• is not gaunt
• is not direct
• is not inverse
• is not discrete

*This also uses the deduced satisfied properties.