One reason for the universal interest in Frobenius algebras is that their characterisation can be formulated in arbitrary categories: a functor K : A → B between categories is Frobenius if there exists a functor G : B → A which is at the same time a right and left adjoint of K; a monad F on A is a Frobenius monad provided the forgetful functor AF → A is a Frobenius functor, where AF denotes the...

Any semi-abelian category A appears, via the discrete functor, as a full replete reflective subcategory of the semi-abelian category of internal groupoids in A. This allows one to study the homology of n-fold internal groupoids with coefficients in a semi-abelian category A, and to compute explicit higher Hopf formulae. The crucial concept making such computations possible is the notion of prot...

We prove that the quadratic second quantization of an operator p on L2(Rd)∩L∞(Rd) is an orthogonal projection on the quadratic Fock space if and only if p = MχI , where MχI is a multiplication operator by a characteristic function χI .