Strongly Involutory Functors |
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Authors: | S Dăscălescu C Năstăsescu M Năstăsescu |
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Institution: | 1. Faculty of Mathematics , University of Bucharest , Bucharest, Romania sdascal2001@yahoo.com;3. Faculty of Mathematics , University of Bucharest , Bucharest, Romania;4. Department of Mathematics , Princeton University , Princeton, New Jersey, USA |
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Abstract: | Let 𝒞 be an arbitrary category. We study strongly involutory functors on 𝒞, defined as involutory contravariant endofunctors of 𝒞 acting as identity on objects. Motivating examples can be constructed if we think at the transpose of a matrix, the adjoint of a linear continuous operator between two Hilbert spaces, and the inverse of a morphism in a groupoid. We show how a strongly involutory functor on a skeleton of 𝒞 extends to 𝒞, and we apply this to find all such functors for a groupoid. We describe and classify up to a natural equivalence all strongly involutory functors on the category of finite dimensional vector spaces over a field. Strongly involutory functors with a special property related to generalized inverses of morphisms are studied. |
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Keywords: | Generalized inverse Involutory functor Vector space |
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