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### 3 operations for triangulated categories

 ‣ AddCounitOfShiftAdjunctionWithGivenObject( C, F ) ( 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. $$F: ( s, r ) \mapsto \mathtt{CounitOfShiftAdjunctionWithGivenObject}(s, r)$$.

 ‣ AddDomainMorphismByOctahedralAxiomWithGivenObjects( C, F ) ( 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. $$F: ( arg2, arg3, arg4, arg5, arg6 ) \mapsto \mathtt{DomainMorphismByOctahedralAxiomWithGivenObjects}(arg2, arg3, arg4, arg5, arg6)$$.

 ‣ AddInverseOfCounitOfShiftAdjunctionWithGivenObject( C, F ) ( 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. $$F: ( s, r ) \mapsto \mathtt{InverseOfCounitOfShiftAdjunctionWithGivenObject}(s, r)$$.

 ‣ AddInverseOfUnitOfShiftAdjunctionWithGivenObject( C, F ) ( 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. $$F: ( s, r ) \mapsto \mathtt{InverseOfUnitOfShiftAdjunctionWithGivenObject}(s, r)$$.

 ‣ AddInverseShiftExpandingIsomorphismWithGivenObjects( C, F ) ( 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. $$F: ( s, L, r ) \mapsto \mathtt{InverseShiftExpandingIsomorphismWithGivenObjects}(s, L, r)$$.

 ‣ AddInverseShiftFactoringIsomorphismWithGivenObjects( C, F ) ( 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. $$F: ( s, L, r ) \mapsto \mathtt{InverseShiftFactoringIsomorphismWithGivenObjects}(s, L, r)$$.

 ‣ AddInverseShiftOfMorphismWithGivenObjects( C, F ) ( 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. $$F: ( s, alpha, r ) \mapsto \mathtt{InverseShiftOfMorphismWithGivenObjects}(s, alpha, r)$$.

 ‣ AddInverseShiftOfObject( C, F ) ( 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. $$F: ( arg2 ) \mapsto \mathtt{InverseShiftOfObject}(arg2)$$.

 ‣ AddIsExactTriangle( C, F ) ( 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. $$F: ( arg2, arg3, arg4 ) \mapsto \mathtt{IsExactTriangle}(arg2, arg3, arg4)$$.

 ‣ AddMorphismBetweenStandardConeObjectsWithGivenObjects( C, F ) ( 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. $$F: ( cone_alpha, list, cone_alpha_prime ) \mapsto \mathtt{MorphismBetweenStandardConeObjectsWithGivenObjects}(cone_alpha, list, cone_alpha_prime)$$.

 ‣ AddMorphismFromConeObjectByOctahedralAxiomWithGivenObjects( C, F ) ( 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. $$F: ( arg2, arg3, arg4, arg5, arg6 ) \mapsto \mathtt{MorphismFromConeObjectByOctahedralAxiomWithGivenObjects}(arg2, arg3, arg4, arg5, arg6)$$.

 ‣ AddMorphismFromStandardConeObject( C, F ) ( 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. $$F: ( alpha ) \mapsto \mathtt{MorphismFromStandardConeObject}(alpha)$$.

 ‣ AddMorphismFromStandardConeObjectWithGivenObjects( C, F ) ( 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. $$F: ( cone_alpha, alpha, sh_source_alpha ) \mapsto \mathtt{MorphismFromStandardConeObjectWithGivenObjects}(cone_alpha, alpha, sh_source_alpha)$$.

 ‣ AddMorphismIntoConeObjectByOctahedralAxiomWithGivenObjects( C, F ) ( 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. $$F: ( arg2, arg3, arg4, arg5, arg6 ) \mapsto \mathtt{MorphismIntoConeObjectByOctahedralAxiomWithGivenObjects}(arg2, arg3, arg4, arg5, arg6)$$.

 ‣ AddMorphismIntoStandardConeObject( C, F ) ( 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. $$F: ( alpha ) \mapsto \mathtt{MorphismIntoStandardConeObject}(alpha)$$.

 ‣ AddMorphismIntoStandardConeObjectWithGivenStandardConeObject( C, F ) ( 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. $$F: ( alpha, cone ) \mapsto \mathtt{MorphismIntoStandardConeObjectWithGivenStandardConeObject}(alpha, cone)$$.

 ‣ AddShiftExpandingIsomorphismWithGivenObjects( C, F ) ( 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. $$F: ( s, L, r ) \mapsto \mathtt{ShiftExpandingIsomorphismWithGivenObjects}(s, L, r)$$.

 ‣ AddShiftFactoringIsomorphismWithGivenObjects( C, F ) ( 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. $$F: ( s, L, r ) \mapsto \mathtt{ShiftFactoringIsomorphismWithGivenObjects}(s, L, r)$$.

 ‣ AddShiftOfMorphismByInteger( C, F ) ( 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. $$F: ( arg2, arg3 ) \mapsto \mathtt{ShiftOfMorphismByInteger}(arg2, arg3)$$.

 ‣ AddShiftOfMorphismByIntegerWithGivenObjects( C, F ) ( 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. $$F: ( arg2, arg3, arg4, arg5 ) \mapsto \mathtt{ShiftOfMorphismByIntegerWithGivenObjects}(arg2, arg3, arg4, arg5)$$.

 ‣ AddShiftOfMorphismWithGivenObjects( C, F ) ( 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. $$F: ( arg2, arg3, arg4 ) \mapsto \mathtt{ShiftOfMorphismWithGivenObjects}(arg2, arg3, arg4)$$.

 ‣ AddShiftOfObject( C, F ) ( 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. $$F: ( arg2 ) \mapsto \mathtt{ShiftOfObject}(arg2)$$.

 ‣ AddShiftOfObjectByInteger( C, F ) ( 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. $$F: ( arg2, arg3 ) \mapsto \mathtt{ShiftOfObjectByInteger}(arg2, arg3)$$.

 ‣ AddStandardConeObject( C, F ) ( 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. $$F: ( arg2 ) \mapsto \mathtt{StandardConeObject}(arg2)$$.

 ‣ AddUnitOfShiftAdjunctionWithGivenObject( C, F ) ( 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. $$F: ( s, r ) \mapsto \mathtt{UnitOfShiftAdjunctionWithGivenObject}(s, r)$$.

 ‣ AddWitnessIsomorphismFromStandardConeObject( C, F ) ( 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. $$F: ( alpha, iota, pi ) \mapsto \mathtt{WitnessIsomorphismFromStandardConeObject}(alpha, iota, pi)$$.

 ‣ AddWitnessIsomorphismFromStandardConeObjectByInverseRotationAxiomWithGivenObjects( C, F ) ( 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. $$F: ( st_cone, f, cone ) \mapsto \mathtt{WitnessIsomorphismFromStandardConeObjectByInverseRotationAxiomWithGivenObjects}(st_cone, f, cone)$$.

 ‣ AddWitnessIsomorphismFromStandardConeObjectByOctahedralAxiomWithGivenObjects( C, F ) ( 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. $$F: ( st_cone, f, g, h, cone_g ) \mapsto \mathtt{WitnessIsomorphismFromStandardConeObjectByOctahedralAxiomWithGivenObjects}(st_cone, f, g, h, cone_g)$$.

 ‣ AddWitnessIsomorphismFromStandardConeObjectByRotationAxiomWithGivenObjects( C, F ) ( 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. $$F: ( st_cone, f, cone ) \mapsto \mathtt{WitnessIsomorphismFromStandardConeObjectByRotationAxiomWithGivenObjects}(st_cone, f, cone)$$.

 ‣ AddWitnessIsomorphismIntoStandardConeObject( C, F ) ( 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. $$F: ( alpha, iota, pi ) \mapsto \mathtt{WitnessIsomorphismIntoStandardConeObject}(alpha, iota, pi)$$.

 ‣ AddWitnessIsomorphismIntoStandardConeObjectByInverseRotationAxiomWithGivenObjects( C, F ) ( 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. $$F: ( cone, f, st_cone ) \mapsto \mathtt{WitnessIsomorphismIntoStandardConeObjectByInverseRotationAxiomWithGivenObjects}(cone, f, st_cone)$$.

 ‣ AddWitnessIsomorphismIntoStandardConeObjectByOctahedralAxiomWithGivenObjects( C, F ) ( 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. $$F: ( cone_g, f, g, h, st_cone ) \mapsto \mathtt{WitnessIsomorphismIntoStandardConeObjectByOctahedralAxiomWithGivenObjects}(cone_g, f, g, h, st_cone)$$.

 ‣ AddWitnessIsomorphismIntoStandardConeObjectByRotationAxiomWithGivenObjects( C, F ) ( operation )
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. $$F: ( cone, f, st_cone ) \mapsto \mathtt{WitnessIsomorphismIntoStandardConeObjectByRotationAxiomWithGivenObjects}(cone, f, st_cone)$$.