category of locally ringed spaces
- notation:
- objects: locally ringed spaces
- morphisms: morphisms of locally ringed spaces, thus consisting of a continuous map and a homomorphism of sheaves that induces local ring homomorphisms in the stalks
- Related categories:
- nLab Link
Satisfied Properties
Properties from the database
- is cocomplete
- is complete
- is infinitary extensive
- is locally small
- is well-copowered
- is well-powered
Deduced properties
- has connected limits
- is finitely complete
- has equalizers
- has coreflexive equalizers
- has products
- has countable products
- has finite products
- has binary products
- has a terminal object
- is connected
- has pullbacks
- is Cauchy complete
- has wide pullbacks
- has cofiltered limits
- has sequential limits
- has powers
- has countable powers
- has finite powers
- has binary powers
- has coproducts
- is extensive
- has finite coproducts
- has a strict initial object
- has an initial object
- has disjoint finite coproducts
- has disjoint coproducts
- is distributive
- is infinitary distributive
- is lextensive
- is locally essentially small
- is inhabited
- has connected colimits
- has sifted colimits
- has filtered colimits
- has reflexive coequalizers
- has directed colimits
- is finitely cocomplete
- 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
Unsatisfied Properties
Properties from the database
- is not balanced
- is not cartesian closed
- is not co-Malcev
- is not Malcev
- is not skeletal
- does not have a strict terminal object
- is not strongly connected
Deduced properties*
- is not a groupoid
- is not mono-regular
- is not direct
- is not discrete
- does not have zero morphisms
- does not have biproducts
- is not pointed
- is not preadditive
- is not additive
- is not abelian
- is not Grothendieck abelian
- is not split abelian
- is not essentially discrete
- is not trivial
- is not thin
- is not left cancellative
- is not one-way
- is not essentially small
- is not small
- is not finite
- is not essentially finite
- is not an elementary topos
- does not have a subobject classifier
- is not locally cartesian closed
- is not a Grothendieck topos
- 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 epi-regular
- is not inverse
- is not counital
- is not self-dual
*This also uses the deduced satisfied properties.
Unknown properties
There are 13 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:
- initial object: empty space
- products: See Localization of ringed spaces by W. Gillam. See also MSE/1033675.
- coproducts: disjoint union with the product sheaf
Special morphisms
- isomorphisms: pairs consisting of a homeomorphism and an isomorphism of sheaves
- monomorphisms:
- epimorphisms:
- regular monomorphisms:
- regular epimorphisms: