Mitsuhiro Takeuchi

Mitsuhiro Takeuchi is a Japanese algebraist. Much of his work is dedicated to bialgebras, Hopf algebras, coalgebras, (co)module algebras, Hopf-Galois extensions and various generalizations of these concepts as well as applications of bialgebras to the theory of algebraic and formal groups and quotients.

He introduced left adjoint to the forgetful functor from Hopf algebras to coalgebras and (by composing) also to the forgetful functor to vector spaces (free Hopf algebra functor), together with a first example of a Hopf algebra with non-bijective antipode in

Takeuchi product of AA-rings (where AA is a noncommutative ring) is named after him, on basis of his fundamental work

Groups of algebras over A×A¯A \times \bar{A}, J. Math. Soc. Japan 29, 459–492, 1977, MR0506407, euclid

Notice that the notation of End vs Coend in the above paper is interchanged (as compared to MacLane’s CWM).

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