Grassmann-Hopf algebroid categories and Grassmann categories
Definition 0.1
The categories whose objects are either
Grassmann-Hopf al/gebras, or in general
algebroids,
and whose morphisms are
homomorphisms are called
Grassmann-Hopf Algebroid Categories.
Although carrying a similar name, a quite different type of Grassmann categories have been
introduced previously:
Definition 0.2
Grassmann Categories (as in [
1]) are defined
on
letters over nontrivial abelian categories

as
full subcategories of the categories

consisting of diagrams satisfying the relations:

and

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
which is isomorphic to the Grassmann-or exterior-ring over
on
letters
.
-
- 1
-
Barry Mitchell.Theory of Categories., Academic Press: New York and London.(1965), pp. 220-221.
- 2
-
B. Fauser: A treatise on quantum Clifford Algebras. Konstanz, Habilitationsschrift. (PDF at arXiv.math.QA/0202059).(2002).
- 3
-
B. Fauser: Grade Free product Formulae from Grassmann-Hopf Gebras., Ch. 18 in R. Ablamowicz, Ed.,
Clifford Algebras: Applications to Mathematics, Physics and Engineering, Birkhäuser: Boston, Basel and Berlin, (2004).
- 4
-
I.C. Baianu, R. Brown J.F. Glazebrook, and G. Georgescu, Towards Quantum Non-Abelian Algebraic Topology. in preparation, (2008).
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