Canon and cannon are very often confused and used improperly. Although the two nouns are pronounced identically and spelled similarly, the only difference being one "n", these words have completely different meanings and should never be used interchangeably in writing.

Cannon (noun): A mounted gun for firing heavy projectiles; a gun, howitzer, or mortar.

A ship's cannon

Example of word in use: Before Darth Vader and his accompanying fighters chased Luke Skywalker in the Death Star's trench, the turbolaser cannons stopped.

A turbolaser cannon

Canon (noun): The body of rules, principles, or standards accepted as axiomatic and universally binding in a field of study or art.

The Chronicle of Narnia canon

Example of word in use: Though the books are numbered, there is still debate over which Narnia book should be read first due to the series' internal chronology.

So to review . . .
Correct Usage:

Women writers have been fighting to find their place within the male-dominated literary canon.
Women writers have been fighting for their place in the male-dominated literary society with cannons. (Grammatically correct, but perhaps not factually correct.)

Incorrect Usage:

The guns are bad enough, but now the enemy has canons!
If you try to put Admiral Thrawn in the new movie, you'll get smacked by Disney because they removed him from the cannon.