Dojo Darelir, the School of Xenograg the Sorcerer

The 6th-century [C.E. Byzantine] soldier was in fact much more than a cavalryman: he had become an all-around mounted warrior. With his bow he could skirmish at a distance, but he was also heavily armoured and well equipped for close mounted combat. When a steady force was needed to hold ground, he was quite happy to dismount and fight as a heavy infantryman. On many occasions Belisarius took only cavalrymen with him, and when Narses needed steady infantry, he dismounted his cavalry.

— Simon MacDowall, Late Roman Cavalryman: 236-565 AD, p. 24

The basis of the [Persian military and political] system [circa 500 B.C.E.] was the spirit, skill, and resourcefulness of the Persians. An important weapon was the bow, used effectively by both cavalry and infantry. Insofar as possible the Persians avoided close-quarters infantry combat until their foes had been thoroughly disorganized by swarms of foot archers from the front, and the daring onrushes of horse archers against flanks and rear. The Persians were versatile in adapting their methods of warfare to all conditions of terrain. They respected the shock action of the Lydian cavalry lancers, and incorporated this concept into their mounted tactics.

Subject peoples were required to render military service. The garrisons scattered throughout the empire were principally composed of unit from other regions…but always contained a Persian contingent. Imperial expeditionary forces were also multinational. The Persians received a surprisingly high standard of loyalty from these diverse peoples, due largely to their policies of leniency toward the conquered, and of carefully supervised but decentralized administration.

— R. Ernest Dupuy and Trevor N. Dupuy, The Encyclopedia of Military History, p. 22

[Bronze Age] composite bows were also notoriously expensive. Such a bow was a very effective weapon, having double or triple the range of a self bow, but its manufacture was costly and difficult (the layering and lamination of wood, horn, and sinew was done at long intervals, and a properly aged bow would leave a bowyer’s shop five or ten years after he had brought in the raw materials from which it was made).

— Robert Drews, The End of the Bronze Age, p. 110

The Byzantine horsed archer was an expert, capable of loosing arrows from either side of the horse while at full gallop, either shooting a fleeing opponent, or defending himself by a ‘Parthian’ shot over the horse’s rearquarters if he himself was fleeing. The method used was a full draw to the right ear which imparted greater poundage to the arrow. The penetrative quality of Roman equipment used at the battle of Callinicum was due to the adoption of the Hunnic bow and the Mongolian release. The Mongolian release, which uses a thumb lock, is faster, whereas the Mediterranean release, using the fingers to draw, is slower and with an oriental bow the fingers would be crushed. Procopius says the bow used by the Persians at Callinicum was much weaker and the arrows unable to pierce armour, even though the rate of delivery was greater.

— Ann Hyland, The Medieval Warhorse, p. 22

Emphasis mine.

With heavy infantry specialized to resist heavy cavalry and light infantry indispensable in sieges and finding its most effective employment in the field against light cavalry, the art of war about the year 1200 [C.E.] had these clearly distinguishable capabilities (using the symbol → to mean was superior to):

heavy infantry → heavy cavalry
heavy cavalry → light infantry
light infantry → light cavalry
light cavalry → both heavy infantry and heavy cavalry.

These relationships are conveniently summarized in schematic [above], in which A means ability to attack successfully in the direction of the arrow and D means ability to defend successfully in the direction of the arrow. Attack includes the capability to compel the attacked to fight; defend implies only the capacity for successful resistance but no ability to force action. The schematic assumes a flat surface.

The ability of the cavalry to dismount modifies this diagram. When the heavy cavalry dismounted it became heavy infantry, and confirmed the generalizations that the man on foot is superior to the mounted man and [that] the defensive is stronger when the same weapon systems confront one another. Light cavalry could gain comparable advantages by dismounting, and in each case the dismounted cavalry in the defense could easily take advantage of terrain or artificial obstacles, something more difficult to do mounted. Medieval soldiers grasped and often exploited the value of dismounting heavy cavalry but, lacking light cavalry, could never make use of this transformation. They did occasionally mount bowmen, giving them the strategic mobility of the light cavalry. They more rarely resorted to a similar mounting of heavy infantry, probably because of their ample supply of heavy cavalry. Yet to have mounted heavy infantry on nags would have been a far more economical solution had knights customarily fought on foot. It would have saved the considerable cost of a robust war horse and the expensive, but unused, skill in fighting mounted.

— Archer Jones, The Art of War in the Western World, p. 145-46