In Shirley Jackson's short story "Charles," the main character is a kindergarten-aged boy named Laurie. The antagonist would be "Charles," a child that Laurie makes up in his imagination. This child, Charles, is a classic antagonist because he bothers people in the classroom, hurts the teacher, and refuses to do anything he is told to do at school.
Laurie talks about Charles everyday as he comes home from school, but it is not until the end of the story that his mother discovers that there is no Charles in the classroom. The reader then assumes that it is Laurie himself, who is misbehaving in class and doing the things that he puts upon the imaginary Charles. Hence, Laurie and Charles are the same person, but are protagonist and antagonist respectively.
The catalyst is the inciting event that throws the main character into the action. Entering kindergarten is one of the catalysts; it is clear that Laurie does not like school, and he is acting up because he has to go.
The theme of the story is identity and how Laurie adheres his bad boy behavior to a made-up character he named "Charles." The name "Charles" is more masculine, sounds more mature, and is more serious than Laurie's name. This is another aspect of the personality of this child. He is distancing himself from the identity that his mother has given him, the image of the innocent kindergartner that needs her love and protection. Instead, he is manifesting as another child, albeit one who does not exist, to excuse his bad behavior.
Finally, the conflict is character versus self and character versus society. Laurie does not enjoy school, and he cannot get along with others. It is clear that he is in direct conflict with his classmates and his society. He is also in a conflict with himself; he cannot come to accept that it is he, Laurie, and not the imaginary Charles, who is doing all these bad things.