No, they don't engage in physical fights before mating. In fact, the female cat usually initiates the mating process by calling to the male, often with loud yowling or meowing. The male will then approach and try to engage her.
There can be a lot of aggression during the mating process itself. This is because the male cat's penis has spines, which can be painful for the female. The female often tries to avoid the male's advances by hissing, scratching, and biting. This can look like a fight, but it's more accurately described as the female trying to control the situation.
Social interactions can lead to aggression. If there are multiple male cats vying for the female's attention, they might engage in some aggressive displays like hissing, posturing, or even a minor scuffle. However, these are typically more about dominance displays than a genuine fight.
Overall, the mating process for cats is more about a complex interplay of hormones and instincts than a physical fight. The female cat is in control of the situation, and she will only accept the male's advances when she is ready.