| 11. | This is essentially equivalent to the commutativity of multiplication.
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| 12. | Functors are represented by arrows between categories, subject to specific defining commutativity conditions.
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| 13. | The only property that presents difficulties to prove is the commutativity of the addition.
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| 14. | The relaxation of this commutativity condition inspires the study of non-commutative geometry.
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| 15. | This can then be used to prove the commutativity of the higher homotopy groups.
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| 16. | By associativity and commutativity, the right-hand sides of these results are equal.
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| 17. | When coded in assembly language, this commutativity is often exercised in the second line:
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| 18. | This explains the commutativity of these operators.
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| 19. | They do not obey commutativity like the quaternions plus they also do not obey associativity.
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| 20. | First delete the commutativity restriction to obtain the concept of a magma or a groupoid.
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