PlanetPhysics/Grassmann Hopf Algebroid Categories and Grassmann Categories

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Grassmann-Hopf Algebroid Categories and Grassmann Categories
The categories whose objects are either Grassmann-Hopf al/gebras, or in general $$G-H$$ algebroids, and whose morphisms are $$G-H$$ homomorphisms are called Grassmann-Hopf Algebroid Categories.

Although carrying a similar name, a quite different type of Grassmann categories have been introduced previously:

Grassmann Categories (as in ) are defined on $$k$$ letters over nontrivial abelian categories $$\mathbf{\A}$$ as full subcategories  of the categories $$F_{\mathbf{\A}}(x_1,...,x_k)$$ consisting of diagrams satisfying the relations: $$x_i x_j + x_j x_i = 0$$ and $$ x_i x_i = 0 $$ with additional conditions on coadjoints, coproducts and morphisms.

They were shown to be equivalent to the category of right modules over the endomorphism ring of the coadjoint $$S(R)$$ which is isomorphic to the Grassmann--or exterior--ring over $$R$$ on $$k$$ letters $$E_R(X_1,..., X_N)$$.