First thought of by a high-ranking but lonely wizard who wanted to keep a part of his dying friend and partner in crime.
He captured a piece of his friends soul upon death and placed it in the hat and all went well for a while.
Sadly a few years after that the creator of the hat died himself `without someone to preserve a piece of his soul.
Since then this hat turned into just another sentient item and is used and worn as such.

It looks a lot like a classic wizard hat but where most are brightly colored this version is white at the top changing to
a fairly dark shade of grey at the bottom. There is a large symbol for eternity embroidered in the front of it.

Add 2 to wisdom of the wearer. Furthermore it is sentient and the way it adds to your wisdom is that it openly
corrects and criticize you when saying something wrong, like an assumption made on a failed wisdom check. It is
never wrong but it doesn't always help you and sometimes when it does it is not really clear what he means.
The hat itself has magical knowledge resulting in you gaining a proficiency in arcana or doubling your arcana
proficiency bonus if you are already proficient.

Hat stats :  Int : 18
                       Wis: 18
                       Cha:16

Alignment : neutral good
Bane: The item seeks to defeat or destroy creatures of a particular kind = favored enemy X3
Favored enemy : Demons, because demons ate his last wearer, also hates mimics because he hates frights, also like most folks...tax collectors.
You have advantage on Wisdom (Survival) checks to track your favored enemies, as well as on Wisdom(Perception,Insight) involving your favored enemies and on Intelligence checks to recall information about them. You also have gain a +2 bonus to damage with weapon attacks, which increases to +3 at 6th level, and +4 at 14th level.

When encountering such a being the hat's intelligence and wisdom score halve and he tries to convince you to attack at once.
Either when the wearer has moved out of sight of the being or it has died the hat regains his normal mental stats.
In he former state the hat will use any means within his capacity and will not hesitate to for instance use personal embarrassing
information to blackmail the wearer into attacking any of his favored enemy.

This version has Favored enemy vs Demons, mimics and tax-collectors but other versions have other favored enemies.
(Dm's discretion) *One of the enemies favored must be the killer of the last wearer.

Notes: Headwear, Sentient