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A poset in which every subset has both a supremum and an infimum.
wp-complete-latticenlab-complete-latticegierz-orderEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Retain the underlying complete lattice of a complete Boolean algebra.
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-complete-latticewp-boolean-algebragierz-orderThis is an authored directed relation from the source endpoint to the target endpoint.
Require every subset to have an infimum and supremum.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-complete-latticegierz-orderEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The supremum and infimum of the empty subset give the least and greatest elements.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-complete-latticewp-bounded-latticegierz-orderThis is an authored directed relation from the source endpoint to the target endpoint.
Require finite meets to distribute over arbitrary joins.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-frame-ordernlab-framegierz-order