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