Each relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
- Relation ID
e_comm_affine- Relation type
- Representation / equivalence
representation-equivalence - Direction
- source → target
- Endpoint roles
- source: Representation / equivalence with; target: Representation / equivalence with
- Authored annotation
- Spec, contravariantly
Authored explanation
The functor Spec gives an anti-equivalence between commutative rings and affine schemes; morphisms reverse direction.
How to interpret this relation type
Reinterpret an object, pass to an equivalent presentation, or relate canonically corresponding structures; the carrier may change.
This is an authored directed relation from the source endpoint to the target endpoint.
- Relation ID
story_prime_spectrum_to_affine_scheme_representation_equivalence- Relation type
- Representation / equivalence
representation-equivalence - Direction
- source → target
- Endpoint roles
- source: Representation / equivalence with; target: Representation / equivalence with
- Authored annotation
- is an affine scheme
Authored explanation
An affine scheme is precisely a locally ringed space isomorphic to Spec(R) for some commutative ring.
How to interpret this relation type
Reinterpret an object, pass to an equivalent presentation, or relate canonically corresponding structures; the carrier may change.
This is an authored directed relation from the source endpoint to the target endpoint.
- Relation ID
scheme_to_affine_scheme- Relation type
- Impose axiom
impose-axiom - Direction
- source → target
- Endpoint roles
- source: Builds toward; target: Built from
- Authored annotation
- + globally affine
Authored explanation
Require the scheme to be isomorphic to Spec(R) for some commutative ring R.
How to interpret this relation type
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.