Feb. 22nd, 2020
(no subject)
Feb. 22nd, 2020 11:25 amThus Kan extensions are simply a method for taking two functors and coming up with a third functor that attempts to make a certain triangle make sense. Requiring this triangle to be commutative is too restrictive, so instead Kan extensions rely on natural transformations to help make the extension be the best possible approximation of F along K.
--- Marina Christina Lehner.
...warfare between the Greek city-states was endemic. Yet from early on in its history Rome’s war-making was distinctive in character, not simply because it was so successful, but through its talent for consolidating success on a permanent basis, as defeated enemies were absorbed and turned into reliable allies.
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Comparatively early on, both Roman and Latin status had lost any real association with particular ethnic or even linguistic groups, and had become primarily legal distinctions. Over time, communities not granted such privileges could hope to gain them, progressing by stages from Latin rights to citizenship without the vote, and finally to full Roman citizenship.
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The most common obligation of all types of ally, including the Latins, was to supply Rome with men and resources in time of war. At least half of any Roman army invariably consisted of allied soldiers. In this way the defeated enemies of the past helped to win the wars of the present. Apart from confirming their loyalty to Rome in this way, the allied communities were also allowed a small, but significant, share in the profits of warfare.
--- Adrian Goldsworthy, Caesar: Life of a Colossus.