Strongly involutory functors

S. Dǎscǎlescu*, C. Nǎstǎsescu, Maria Monica Nastasescu

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1677-1689
Number of pages13
JournalCommunications in Algebra
Volume37
Issue number5
DOIs
StatePublished - May 2009

Keywords

  • Generalized inverse
  • Involutory functor
  • Vector space

ASJC Scopus subject areas

  • Algebra and Number Theory

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