The First War of The Diadochi
To a good general luck is important.-Livy
Ptolemy's act was essentially a declaration of war. When war broke out, it was clear Perdiccas was going to go after Ptolemy in Egypt first. He had taken the corpse to Memphis for the time being, as Alexandria was still one giant construction project. Alexander's corpse was to valuable to Ptolemy to be resting at the oasis in Siwah.
This also had the inadvertent effect of saving Craterus from having his troops commandeered by Perdiccas. In the summer of 321, Perdiccas had summoned Antigonus to Sardis to question why he disobeyed orders. Perdiccas had unknowingly insulted Menander however, satrap of Lydia, whose capital was in Sardis.
Perdiccas had flattered Cleopatra (who had been used to being queen of Molossia for some years after her husbands death) by putting her in charge of Lydia, and demoting Menander to her second in command, only responsible for the military. Menander explained to Antigonus and Craterus that Perdiccas was actively courting Cleopatra,and had accepted the inevitability of war. Antigonus, who had already decided he would not side with Perdiccas when war came, fled to Craterus instead of going to Perdiccas' summons, which almost would have certainly lead to his premature death.
Craterus and Antigonus prepared for war, in Hellespontine Phrygia They wrote to Ptolemy, receiving encouraging news about his intentions. Perdiccas would be fighting a two front war.
Antigonus and Craterus immediately opted for a treaty with the Greeks, wanting the seas open. Perdiccas had been one step ahead of them however, and had already courted the Greeks into using their navy to his advantage. War seemed inevitable. It was the hijacking of the corpse by Ptolemy that finally triggered it.
Perdiccas knew Craterus and and Antigonus were going to launch an attack on the rest of Asia Minor. Why he hadn't done anything about Craterus earlier, while he was still vulnerable in Hellespontine Phrygia, is not known. However, it is clear Perdiccas had a score to settle with Ptolemy, so he had decided to go fight Ptolemy in Egypt personally. He left Eumenes in command of a force of 20,000, with orders to Alcetas and Neoptolemus to join him (Eumenes). Cleitus was also given command of what was left of the fleet, though he would defect back to Craterus shortly.
Antigonus went ahead and immediately won the defections of Caria and Lydia. Menander and Asander (the satraps of Lydia and Caria respectively,) both had thier reasons for defecting, Asander being an old ally of Antigonus, and Menander feeling slighted by Perdiccas. Eumenes was caught by surprise, and was nearly trapped in Sardis, with only Cleopatra's warning allowing him to escape.
The loyalist cause was falling apart in Anatolia before it had much of a chance. Alcetas, fearing his troops would simply refuse to fight the extremely popular Craterus, declared neutrality for the moment, preferring to wait it out. Neoptolemus began secret negotiations with Craterus. Everything rested on the shoulders of the untested little Eumenes.
Eumenes pulled back to the borders of Cappadocia. Antigonus' and Craterus' plans were simple.Antigonus now went south, to Cilicia, with him and Craterus splitting up their forces. Craterus was to annihilate Eumenes, and Antigonus was to occupy Cilicia, before the two were to join up again and trap Perdiccas between their and Ptolemy's forces.
Neoptolemus now attempted to join Craterus as a friend instead of a foe, but was confronted by Eumenes, who was one step ahead of him. A battle broke out in late May of 320, and was a victory for Eumenes, who captured Neoptolemus' baggage train. Neoptolemus fled to Craterus with only a small cavalry force, Eumenes now in control of his infantry.
When battle ensued, Eumenes showed the first signs of his brilliance. He had gone through great pains to conceal that Craterus was the enemy commander, and instead convinced them it was Neoptolemus. To increase morale, he explained Alexander had promised him victory in a dream. It was all he could do, for he knew that if the battle came between the two infantry phalanxes, his men would likely desert.
Eumenes was not about to let that happen. He had a significant cavalry advantage, and intended to exploit it to the best of his ability. While his phalanx was deploying, he sent the Cappadocian cavalry forward, sweeping the enemy cavalry from the field, and in a stroke of luck, Craterus fell of his horse and was trampled to death. Meanwhile on the other wing, Eumenes killed Neoptolemus in a brutal hand to hand fight himself, the mutual loathing between the two, leading to them pulling each other off their horses and tumbling to the ground, before Eumenes dispatched his adversary.
Eumenes now sent one of his officers to address the opposing phalangites, sending the message that "We won't fight if you don't". The enemy phalangites surrendered and swelled Eumenes ranks. They attempted to slip away at night, but Eumenes was one step ahead of them. A significant portion of them managed to escape to Antigonus, but many of them were caught by Eumenes, preventing them from escaping.[1]
[1] In OTL they all escaped to Antipater.