Formatting
]]>Minor fixes
]]>I am writing an explicit definition of a left bialgebroid for the wikipedia in a different way than I previously put into the entry so I am copying a variant here to have yet another equivalent definition, avoiding -rings.
]]>Some new material at bialgebroid, following
All modules and morphisms will be over a fixed ground commutative ring .
A left -bialgebroid is an -ring , together with the -bimodule map , which is coassociative and counital with counit , such that
(i) the -bimodule structure used on is , where and are the algebra maps induced by the unit of the -ring
(ii) the coproduct corestricts to the Takeuchi product and the corestriction is a -algebra map, where the Takeuchi product has a multiplication induced factorwise
(iii) is a left character on the -ring
Notice that is in general not an algebra, just an -bimodule.
The definition of a right -bialgebroid differs by the -bimodule structure on given instead by and the counit is a right character on the -coring ( and can be interchanged in the last requirement).
]]>Related new stubs dynamical extension of a monoidal category and dynamical Yang-Baxter equation.
]]>The stub for “associative” bialgebroid. Bialgebroids are to bialgebras what on dual side groupoids are to groups. More references at Hopf algebroids.
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