In mathematics, an internal bialgebroid is a structure which generalizes the notion of an associative bialgebroid to the setup where the ambient symmetric monoidal category of vector spaces is replaced by any abstract symmetric monoidal category (C, , I,s) admitting coequalizers commuting with the monoidal product . It consists of two monoids in the monoidal category (C, , I), namely the base monoid and the total monoid , and several structure morphisms involving and as first axiomatized by G. Böhm. The coequalizers are needed to introduce the tensor product of (internal) bimodules over the base monoid; this tensor product is consequently (a part of) a monoidal structure on the category of -bimodules. In the axiomatics, appears to be an -bimodule in a specific way. One of the structur