‣ AddCounitOfShiftAdjunctionWithGivenObject( C, F ) | ( operation ) |
‣ AddCounitOfShiftAdjunctionWithGivenObject( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CounitOfShiftAdjunctionWithGivenObject. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( s, r ) \mapsto \mathtt{CounitOfShiftAdjunctionWithGivenObject}(s, r)\).
‣ AddDomainMorphismByOctahedralAxiomWithGivenObjects( C, F ) | ( operation ) |
‣ AddDomainMorphismByOctahedralAxiomWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation DomainMorphismByOctahedralAxiomWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( arg2, arg3, arg4, arg5, arg6 ) \mapsto \mathtt{DomainMorphismByOctahedralAxiomWithGivenObjects}(arg2, arg3, arg4, arg5, arg6)\).
‣ AddInverseOfCounitOfShiftAdjunctionWithGivenObject( C, F ) | ( operation ) |
‣ AddInverseOfCounitOfShiftAdjunctionWithGivenObject( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InverseOfCounitOfShiftAdjunctionWithGivenObject. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( s, r ) \mapsto \mathtt{InverseOfCounitOfShiftAdjunctionWithGivenObject}(s, r)\).
‣ AddInverseOfUnitOfShiftAdjunctionWithGivenObject( C, F ) | ( operation ) |
‣ AddInverseOfUnitOfShiftAdjunctionWithGivenObject( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InverseOfUnitOfShiftAdjunctionWithGivenObject. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( s, r ) \mapsto \mathtt{InverseOfUnitOfShiftAdjunctionWithGivenObject}(s, r)\).
‣ AddInverseShiftExpandingIsomorphismWithGivenObjects( C, F ) | ( operation ) |
‣ AddInverseShiftExpandingIsomorphismWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InverseShiftExpandingIsomorphismWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( s, L, r ) \mapsto \mathtt{InverseShiftExpandingIsomorphismWithGivenObjects}(s, L, r)\).
‣ AddInverseShiftFactoringIsomorphismWithGivenObjects( C, F ) | ( operation ) |
‣ AddInverseShiftFactoringIsomorphismWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InverseShiftFactoringIsomorphismWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( s, L, r ) \mapsto \mathtt{InverseShiftFactoringIsomorphismWithGivenObjects}(s, L, r)\).
‣ AddInverseShiftOfMorphismWithGivenObjects( C, F ) | ( operation ) |
‣ AddInverseShiftOfMorphismWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InverseShiftOfMorphismWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( s, alpha, r ) \mapsto \mathtt{InverseShiftOfMorphismWithGivenObjects}(s, alpha, r)\).
‣ AddInverseShiftOfObject( C, F ) | ( operation ) |
‣ AddInverseShiftOfObject( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InverseShiftOfObject. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( arg2 ) \mapsto \mathtt{InverseShiftOfObject}(arg2)\).
‣ AddIsExactTriangle( C, F ) | ( operation ) |
‣ AddIsExactTriangle( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsExactTriangle. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( arg2, arg3, arg4 ) \mapsto \mathtt{IsExactTriangle}(arg2, arg3, arg4)\).
‣ AddMorphismBetweenStandardConeObjectsWithGivenObjects( C, F ) | ( operation ) |
‣ AddMorphismBetweenStandardConeObjectsWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismBetweenStandardConeObjectsWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( cone_alpha, list, cone_alpha_prime ) \mapsto \mathtt{MorphismBetweenStandardConeObjectsWithGivenObjects}(cone_alpha, list, cone_alpha_prime)\).
‣ AddMorphismFromConeObjectByOctahedralAxiomWithGivenObjects( C, F ) | ( operation ) |
‣ AddMorphismFromConeObjectByOctahedralAxiomWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismFromConeObjectByOctahedralAxiomWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( arg2, arg3, arg4, arg5, arg6 ) \mapsto \mathtt{MorphismFromConeObjectByOctahedralAxiomWithGivenObjects}(arg2, arg3, arg4, arg5, arg6)\).
‣ AddMorphismFromStandardConeObject( C, F ) | ( operation ) |
‣ AddMorphismFromStandardConeObject( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismFromStandardConeObject. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( alpha ) \mapsto \mathtt{MorphismFromStandardConeObject}(alpha)\).
‣ AddMorphismFromStandardConeObjectWithGivenObjects( C, F ) | ( operation ) |
‣ AddMorphismFromStandardConeObjectWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismFromStandardConeObjectWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( cone_alpha, alpha, sh_source_alpha ) \mapsto \mathtt{MorphismFromStandardConeObjectWithGivenObjects}(cone_alpha, alpha, sh_source_alpha)\).
‣ AddMorphismIntoConeObjectByOctahedralAxiomWithGivenObjects( C, F ) | ( operation ) |
‣ AddMorphismIntoConeObjectByOctahedralAxiomWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismIntoConeObjectByOctahedralAxiomWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( arg2, arg3, arg4, arg5, arg6 ) \mapsto \mathtt{MorphismIntoConeObjectByOctahedralAxiomWithGivenObjects}(arg2, arg3, arg4, arg5, arg6)\).
‣ AddMorphismIntoStandardConeObject( C, F ) | ( operation ) |
‣ AddMorphismIntoStandardConeObject( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismIntoStandardConeObject. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( alpha ) \mapsto \mathtt{MorphismIntoStandardConeObject}(alpha)\).
‣ AddMorphismIntoStandardConeObjectWithGivenStandardConeObject( C, F ) | ( operation ) |
‣ AddMorphismIntoStandardConeObjectWithGivenStandardConeObject( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismIntoStandardConeObjectWithGivenStandardConeObject. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( alpha, cone ) \mapsto \mathtt{MorphismIntoStandardConeObjectWithGivenStandardConeObject}(alpha, cone)\).
‣ AddShiftExpandingIsomorphismWithGivenObjects( C, F ) | ( operation ) |
‣ AddShiftExpandingIsomorphismWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ShiftExpandingIsomorphismWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( s, L, r ) \mapsto \mathtt{ShiftExpandingIsomorphismWithGivenObjects}(s, L, r)\).
‣ AddShiftFactoringIsomorphismWithGivenObjects( C, F ) | ( operation ) |
‣ AddShiftFactoringIsomorphismWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ShiftFactoringIsomorphismWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( s, L, r ) \mapsto \mathtt{ShiftFactoringIsomorphismWithGivenObjects}(s, L, r)\).
‣ AddShiftOfMorphismByInteger( C, F ) | ( operation ) |
‣ AddShiftOfMorphismByInteger( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ShiftOfMorphismByInteger. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( arg2, arg3 ) \mapsto \mathtt{ShiftOfMorphismByInteger}(arg2, arg3)\).
‣ AddShiftOfMorphismByIntegerWithGivenObjects( C, F ) | ( operation ) |
‣ AddShiftOfMorphismByIntegerWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ShiftOfMorphismByIntegerWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( arg2, arg3, arg4, arg5 ) \mapsto \mathtt{ShiftOfMorphismByIntegerWithGivenObjects}(arg2, arg3, arg4, arg5)\).
‣ AddShiftOfMorphismWithGivenObjects( C, F ) | ( operation ) |
‣ AddShiftOfMorphismWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ShiftOfMorphismWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( arg2, arg3, arg4 ) \mapsto \mathtt{ShiftOfMorphismWithGivenObjects}(arg2, arg3, arg4)\).
‣ AddShiftOfObject( C, F ) | ( operation ) |
‣ AddShiftOfObject( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ShiftOfObject. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( arg2 ) \mapsto \mathtt{ShiftOfObject}(arg2)\).
‣ AddShiftOfObjectByInteger( C, F ) | ( operation ) |
‣ AddShiftOfObjectByInteger( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ShiftOfObjectByInteger. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( arg2, arg3 ) \mapsto \mathtt{ShiftOfObjectByInteger}(arg2, arg3)\).
‣ AddStandardConeObject( C, F ) | ( operation ) |
‣ AddStandardConeObject( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation StandardConeObject. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( arg2 ) \mapsto \mathtt{StandardConeObject}(arg2)\).
‣ AddUnitOfShiftAdjunctionWithGivenObject( C, F ) | ( operation ) |
‣ AddUnitOfShiftAdjunctionWithGivenObject( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UnitOfShiftAdjunctionWithGivenObject. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( s, r ) \mapsto \mathtt{UnitOfShiftAdjunctionWithGivenObject}(s, r)\).
‣ AddWitnessIsomorphismFromStandardConeObject( C, F ) | ( operation ) |
‣ AddWitnessIsomorphismFromStandardConeObject( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation WitnessIsomorphismFromStandardConeObject. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( alpha, iota, pi ) \mapsto \mathtt{WitnessIsomorphismFromStandardConeObject}(alpha, iota, pi)\).
‣ AddWitnessIsomorphismFromStandardConeObjectByInverseRotationAxiomWithGivenObjects( C, F ) | ( operation ) |
‣ AddWitnessIsomorphismFromStandardConeObjectByInverseRotationAxiomWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation WitnessIsomorphismFromStandardConeObjectByInverseRotationAxiomWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( st_cone, f, cone ) \mapsto \mathtt{WitnessIsomorphismFromStandardConeObjectByInverseRotationAxiomWithGivenObjects}(st_cone, f, cone)\).
‣ AddWitnessIsomorphismFromStandardConeObjectByOctahedralAxiomWithGivenObjects( C, F ) | ( operation ) |
‣ AddWitnessIsomorphismFromStandardConeObjectByOctahedralAxiomWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation WitnessIsomorphismFromStandardConeObjectByOctahedralAxiomWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( st_cone, f, g, h, cone_g ) \mapsto \mathtt{WitnessIsomorphismFromStandardConeObjectByOctahedralAxiomWithGivenObjects}(st_cone, f, g, h, cone_g)\).
‣ AddWitnessIsomorphismFromStandardConeObjectByRotationAxiomWithGivenObjects( C, F ) | ( operation ) |
‣ AddWitnessIsomorphismFromStandardConeObjectByRotationAxiomWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation WitnessIsomorphismFromStandardConeObjectByRotationAxiomWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( st_cone, f, cone ) \mapsto \mathtt{WitnessIsomorphismFromStandardConeObjectByRotationAxiomWithGivenObjects}(st_cone, f, cone)\).
‣ AddWitnessIsomorphismIntoStandardConeObject( C, F ) | ( operation ) |
‣ AddWitnessIsomorphismIntoStandardConeObject( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation WitnessIsomorphismIntoStandardConeObject. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( alpha, iota, pi ) \mapsto \mathtt{WitnessIsomorphismIntoStandardConeObject}(alpha, iota, pi)\).
‣ AddWitnessIsomorphismIntoStandardConeObjectByInverseRotationAxiomWithGivenObjects( C, F ) | ( operation ) |
‣ AddWitnessIsomorphismIntoStandardConeObjectByInverseRotationAxiomWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation WitnessIsomorphismIntoStandardConeObjectByInverseRotationAxiomWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( cone, f, st_cone ) \mapsto \mathtt{WitnessIsomorphismIntoStandardConeObjectByInverseRotationAxiomWithGivenObjects}(cone, f, st_cone)\).
‣ AddWitnessIsomorphismIntoStandardConeObjectByOctahedralAxiomWithGivenObjects( C, F ) | ( operation ) |
‣ AddWitnessIsomorphismIntoStandardConeObjectByOctahedralAxiomWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation WitnessIsomorphismIntoStandardConeObjectByOctahedralAxiomWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( cone_g, f, g, h, st_cone ) \mapsto \mathtt{WitnessIsomorphismIntoStandardConeObjectByOctahedralAxiomWithGivenObjects}(cone_g, f, g, h, st_cone)\).
‣ AddWitnessIsomorphismIntoStandardConeObjectByRotationAxiomWithGivenObjects( C, F ) | ( operation ) |
‣ AddWitnessIsomorphismIntoStandardConeObjectByRotationAxiomWithGivenObjects( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation WitnessIsomorphismIntoStandardConeObjectByRotationAxiomWithGivenObjects. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( cone, f, st_cone ) \mapsto \mathtt{WitnessIsomorphismIntoStandardConeObjectByRotationAxiomWithGivenObjects}(cone, f, st_cone)\).
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