A Categorical Proof of a Useful Result

Abstract

We give a categorical proof of the following equality

$$ \bigcap\limits_{i = 0}^n {\left( {V \otimes V_{n - i} + V_i \otimes V} \right) = } \sum\limits_{i = 1}^n {V_i \otimes V_{n + 1 - i} } $$

which holds for any chain {0} = V ₀ ⊆ V ₁ ⊆ V ₂ ⊆ ... of subspaces of space V.

This paper was written while both the authors were members of G.N.S.A.G.A. with partial financial support from M.i.U.R..