Karna's rival in Ancient Indian epic poem, the Mahabharata… Or rather, story-wise, Karna is the rival and Arjuna is the one who is in the position of protagonist. He is Karna's younger half-brother, but Arjuna continued to fight Karna without ever knowing that.
He has an honest and faithful personality that seems to embody justice itself. (At the very least, the people around him, including Karna, perceived him that way.)
Both in the present as a summoned Servant and in his lifetime, Karna lived without fussing over anything, but the only thing that the detached Karna ever felt an obsession towards was Arjuna.
Even when his mother Kunti begged him not to fight his five younger brothers, including Arjuna, Karna swore to not fight any of them except for Arjuna. Even for his mother's request, Arjuna was something to Karna that he couldn't turn over.
And it was the same for Arjuna as well. To him, Karna was—
…These two will probably be told of in another work someday. At least, it would be nice if that happened.

Fate/Apocrypha material: Fate/Apocrypha Encylopedia