how a fighter moves
Fighter is the default ground enemy behavior, and most of what you kill in a normal night is running it. The enemy picks the shortest line to your character and walks it, hopping small ledges and gaps along the way. The part that matters in play is that it steers toward your height as hard as it steers toward your position, so it will climb, drop and fall through platforms trying to get level with you. Nothing about the path is clever. A fighter has no idea the floor ends until it is already standing on the edge.
doors will not stop them
Most fighters can shove a door open after standing in front of it for about two seconds, and a tall gate after roughly five. A few are faster. Angry Bones need one second for a door and two for a gate, and the Butcher takes one second for either. The Goblin Thief does not open doors at all, it destroys them, which is why a goblin army leaves your house full of empty frames. Some enemies can only work doors during a Blood Moon.
The timer only advances while the enemy stays put. Push it off the door with knockback and the count goes back to zero, so five interrupted swings at a gate still leaves the gate closed.
when a door actually holds
A door only opens if three things are true at that moment: the enemy has no vertical momentum, the tile above its head is not solid, and the tile it is standing on has a flat top. Half blocks, floor slopes, stairs and bottom platforms all fail the last check, so a doorway approached over sloped ground holds against everything except a goblin. The swing direction matters too. A door needs clear space on the side it opens toward, so a work bench or a placed block directly behind it locks it permanently.
the platform pit
Because fighters chase your vertical position, you can build a trap out of nothing but platforms. Dig a pit, run a platform bridge over the top of it, and stand at the bottom. Enemies crossing the bridge read you as below them and drop straight through into the hole. The same instinct works against them in an arena, where a fighter will jump at the ledge you are standing on over and over instead of walking to the ramp two tiles away.
fighting them
Flat ground is worth more than any single item here. On level terrain fighters arrive at a predictable height and stack into a line on their own, which is the whole reason piercing weapons feel far stronger against a crowd of them than against anything else. Knockback covers the rest, since an enemy being shoved is not swinging.
Confusion is the hard counter. A confused fighter turns and walks the other way, and the ranged ones stop firing while it lasts, which turns a pack of Skeleton Archer into a harmless crowd until the debuff wears off.
who runs it
The list covers far more than the obvious melee mobs. Ordinary zombies and skeletons use it, but so do heavy late-game threats like Paladin, Bone Lee, Ice Golem and Possessed Armor, along with every archer and gunner enemy that shoots at you while walking. If it is on this list, the pit trick and the confusion trick both work on it.