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A preorder in which mutual comparability forces equality.
wp-posetnlab-partial-ordergierz-orderEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
On a DAG, define when is reachable from ; adding reflexivity yields a partial order.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
wp-dagwp-posetgierz-orderThis is an authored directed relation from the source endpoint to the target endpoint.
Require and to imply .
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-posetgierz-orderEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Select posets in which bottom and top exist; each is unique.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-bounded-posetgierz-orderThis is an authored directed relation from the source endpoint to the target endpoint.
Require every directed subset to have a supremum.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-cponlab-dcpogierz-orderThis is an authored directed relation from the source endpoint to the target endpoint.
Require every pair to have a least upper bound.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-semilatticegierz-orderThis is an authored directed relation from the source endpoint to the target endpoint.
Require every pair to have a greatest lower bound.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-semilatticegierz-orderThis is an authored directed relation from the source endpoint to the target endpoint.
A map becomes monotone after specifying ordered domain and codomain and requiring that every order comparison in the domain is preserved in the codomain.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
gierz-orderThis is an authored directed relation from the source endpoint to the target endpoint.
Require each pair to be comparable.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-total-ordergierz-order