Lattices are thin, finite cartesian (and hence finite complete), finite cocartesian (and hence finite cocomplete), skeletal categories.
‣ IsCartesianProset( C ) | ( property ) |
Returns: true or false
The property of C being a cartesian proset.
‣ IsMeetSemiLattice( C ) | ( property ) |
Returns: true or false
The property of C being a meet semi-lattice.
‣ IsCocartesianProset( C ) | ( property ) |
Returns: true or false
The property of C being a finite cocomplete proset.
‣ IsJoinSemiLattice( C ) | ( property ) |
Returns: true or false
The property of C being a join semi-lattice.
‣ IsBicartesianProset( C ) | ( property ) |
Returns: true or false
The property of C being a finite complete and cocomplete proset.
‣ IsLattice( C ) | ( property ) |
Returns: true or false
The property of C being a lattice.
‣ IsDistributiveBicartesianProset( C ) | ( property ) |
Returns: true or false
The property of C being a distributive (and automatically codistributive) bicartesian proset.
‣ IsDistributiveLattice( C ) | ( property ) |
Returns: true or false
The property of C being a distributive (and automatically codistributive) lattice.
‣ IsMonoidalLattice( C ) | ( property ) |
Returns: true or false
The property of C being a monoidal lattice.
‣ IsClosedMonoidalLattice( C ) | ( property ) |
Returns: true or false
The property of C being a closed monoidal lattice.
‣ IsCoclosedMonoidalLattice( C ) | ( property ) |
Returns: true or false
The property of C being a coclosed monoidal lattice.
‣ Factors( A ) | ( operation ) |
Returns: a list
Compute the "factors" of A. This is a list C with the minimum specification that DirectProduct(L)=A.
‣ FactorsAttr( arg ) | ( attribute ) |
3.3-1 \*‣ \*( A, B ) | ( operation ) |
Returns: an object in a meet semilattice
The meet DirectProduct(A, B) of A and B.
3.3-2 \+‣ \+( A, B ) | ( operation ) |
Returns: an object in a join semilattice
The join Coproduct(A, B) of A and B.
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