Symmetric Self-Adjunctions and Matrices

Details Symmetric Self-Adjunctions and Matrices Symmetric Self-Adjunctions and Matrices

2005-10-03

arxiv.org/abs/math/0510039v9

Mathematics

Category Theory

40 pages

Scientific paper

It is shown that the multiplicative monoids of Brauer's centralizer algebras generated out of the basis are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself, and where, moreover, a kind of symmetry involving the self-adjoint functor is satisfied. As in a previous paper, of which this is a companion, it is shown that such a symmetric self-adjunction is found in a category whose arrows are matrices, and the functor adjoint to itself is based on the Kronecker product of matrices.

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