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Selfadjunctions and matrices
 Journal of Pure and Applied Algebra
"... It is shown that the multiplicative monoids of TemperleyLieb algebras are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself. Such a selfadjunction is found in a category whose arrows are matrices, and the functor adjoint to itself is based on the Kronec ..."
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Cited by 10 (4 self)
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It is shown that the multiplicative monoids of TemperleyLieb algebras are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself. Such a selfadjunction is found in a category whose arrows are matrices, and the functor adjoint to itself is based on the Kronecker product of matrices. Thereby one obtains a representation of braid groups in matrices, which, though different and presumably new, is related to the standard representation of braid groups in TemperleyLieb algebras. Mathematics Subject Classification (2000): 57M99, 20F36, 18A40 1
unknown title
, 2003
"... A presentation by generators and relations is given for the monoids of endomorphisms in the simplicial category. These monoids are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to its ..."
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A presentation by generators and relations is given for the monoids of endomorphisms in the simplicial category. These monoids are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of simplicial endomorphisms axiomatized here are linked to arbitrary adjoint situations. This link is established through diagrams of the kind found in TemperleyLieb algebras.
unknown title
, 2003
"... A presentation by generators and relations is given for the monoids of endomorphisms in the simplicial category. These monoids are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to its ..."
Abstract
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A presentation by generators and relations is given for the monoids of endomorphisms in the simplicial category. These monoids are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of simplicial endomorphisms axiomatized here are linked to arbitrary adjoint situations. This link is established through diagrams of the kind found in TemperleyLieb algebras.
unknown title
, 2007
"... The monoids of simplicial endomorphisms, i.e. the monoids of endomorphisms in the simplicial category, are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of s ..."
Abstract
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The monoids of simplicial endomorphisms, i.e. the monoids of endomorphisms in the simplicial category, are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of simplicial endomorphisms are linked to arbitrary adjoint situations. This link is established through diagrams of the kind found in TemperleyLieb algebras. Results about these matters, which were previously prefigured up to a point, are here surveyed and reworked. A presentation of monoids of simplicial endomorphisms by generators and relations has been given a long time ago. Here a closely related presentation is given, with completeness proved in a new and selfcontained manner.
unknown title
, 2003
"... A presentation by generators and relations is given for the monoids of endomorphisms in the simplicial category. These monoids are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to its ..."
Abstract
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A presentation by generators and relations is given for the monoids of endomorphisms in the simplicial category. These monoids are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of simplicial endomorphisms axiomatized here are linked to arbitrary adjoint situations. This link is established through diagrams of the kind found in TemperleyLieb algebras.
unknown title
, 2003
"... A presentation by generators and relations is given for the monoids of endomorphisms in the simplicial category. These monoids are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to its ..."
Abstract
 Add to MetaCart
A presentation by generators and relations is given for the monoids of endomorphisms in the simplicial category. These monoids are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of simplicial endomorphisms axiomatized here are linked to arbitrary adjoint situations. This link is established through diagrams of the kind found in TemperleyLieb algebras.
unknown title
, 2007
"... The monoids of simplicial endomorphisms, i.e. the monoids of endomorphisms in the simplicial category, are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of s ..."
Abstract
 Add to MetaCart
The monoids of simplicial endomorphisms, i.e. the monoids of endomorphisms in the simplicial category, are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of simplicial endomorphisms are linked to arbitrary adjoint situations. This link is established through diagrams of the kind found in TemperleyLieb algebras. Results about these matters, which were previously prefigured up to a point, are here surveyed and reworked. A presentation of monoids of simplicial endomorphisms by generators and relations has been given a long time ago. Here a closely related presentation is given, with completeness proved in a new and selfcontained manner.
unknown title
, 2003
"... A presentation by generators and relations is given for the monoids of endomorphisms in the simplicial category. These monoids are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to its ..."
Abstract
 Add to MetaCart
A presentation by generators and relations is given for the monoids of endomorphisms in the simplicial category. These monoids are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of simplicial endomorphisms axiomatized here are linked to arbitrary adjoint situations. This link is established through diagrams of the kind found in TemperleyLieb algebras.
unknown title
, 2007
"... The monoids of simplicial endomorphisms, i.e. the monoids of endomorphisms in the simplicial category, are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of s ..."
Abstract
 Add to MetaCart
The monoids of simplicial endomorphisms, i.e. the monoids of endomorphisms in the simplicial category, are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of simplicial endomorphisms are linked to arbitrary adjoint situations. This link is established through diagrams of the kind found in TemperleyLieb algebras. Results about these matters, which were previously prefigured up to a point, are here surveyed and reworked. A presentation of monoids of simplicial endomorphisms by generators and relations has been given a long time ago. Here a closely related presentation is given, with completeness proved in a new and selfcontained manner.
unknown title
, 2007
"... The monoids of simplicial endomorphisms, i.e. the monoids of endomorphisms in the simplicial category, are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of s ..."
Abstract
 Add to MetaCart
The monoids of simplicial endomorphisms, i.e. the monoids of endomorphisms in the simplicial category, are submonoids of monoids one finds in TemperleyLieb algebras, and as the monoids of TemperleyLieb algebras are linked to situations where an endofunctor is adjoint to itself, so the monoids of simplicial endomorphisms are linked to arbitrary adjoint situations. This link is established through diagrams of the kind found in TemperleyLieb algebras. Results about these matters, which were previously prefigured up to a point, are here surveyed and reworked. A presentation of monoids of simplicial endomorphisms by generators and relations has been given a long time ago. Here a somewhat different related presentation is given, with completeness proved in a new and selfcontained manner.