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A function between partially ordered sets that preserves order: implies .
gierz-orderriehl-category-contextEach relation below ends at this concept.
This 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-orderEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
A Galois connection adds a second monotone map in the reverse direction and the adjoint equivalence .
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-orderriehl-category-context