nLab 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.

• A simple proof of Gabriel and Popesco’s theorem, J. Alg. 18, 112–113 (1971) pdf
• H. F. Kreimer, M. Takeuchi, Hopf algebras and Galois extensions of an algebra, Indiana Univ. Math. J. 30 (1981), 615-692 web pdf djvu
• Stefaan Caenepeel, Septimiu Crivei, Andrei Marcus, Mitsuhiro Takeuchi, Morita equivalences induced by bimodules over Hopf–Galois extensions, J. Algebra 314 (2007) 267–302 pdf
• Y. Doi, Mitsuhiro Takeuchi, Cleft comodule algebras for a bialgebra, Comm. Alg. 14 (1986) 801–818 doi
• M. Takeuchi, Matched pairs of groups and bismash products of Hopf algebras, Comm. Alg. 9:8 (1981) 841–882 doi

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

• Free Hopf algebras generated by coalgebras, J. Math. Soc. Japan 23:4 (1971) 561–582

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

Groups of algebras over $A \times \bar{A}$, 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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