Coalgebra Structures
The tensor algebra has two coalgebra structures; one simple one, which does not make it a bialgebra, and a more complicated one, which yields a bialgebra, and can be extended with an antipode to a Hopf algebra structure.
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“The philosopher believes that the value of his philosophy lies in its totality, in its structure: posterity discovers it in the stones with which he built and with which other structures are subsequently built that are frequently betterand so, in the fact that that structure can be demolished and yet still possess value as material.”
—Friedrich Nietzsche (18441900)
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