Growing Stronger
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Apparently, Material-type Monsters exists in this world, somewhere. I would guess they're like a type of Cursed Item that fight on their own, maybe they could be classified as Undead as a soul inhabits them, but they're classified as "Material" anyways. I wonder what other Material-type Spirits could be acquired… Perhaps a Golem, maybe? How about a Living Armor? Hm, the possibilities are certainly endless, and they're strong too.
The only weakness Ax possess is that it cannot move on its own. It lacks Telekinesis to lift itself up, so when it is summoned, it usually just falls over the floor. Also, it has an HP which is the durability, so when it receives enough hits, it disappears. Making it frailer than normal weapons, perhaps.