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Bireflectivity

Freyd, PJ; O'Hearn, PW; Power, AJ; Takeyama, M; Tennent, RD; (1995) Bireflectivity. Electronic Notes in Theoretical Computer Science , 1 (C) pp. 199-213. 10.1016/S1571-0661(04)80011-2.

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Abstract

Motivated by a model for syntactic control of interference, we introduce a general categorical concept of bireflectivity. Bireflective subcategories of a category A are subcategories with left and right adjoint equal, subject to a coherence condition. We characterize them in terms of split-idempotent natural transformations on idA. In the special case that A is a presheaf category, we characterize them in terms of the domain, and prove that any bireflective subcategory of A is itself a presheaf category. Given a small symmetric monoidal category C, we define diagonal structure on C, which is that structure and a little less than those axioms required to prove the monoidal structure is finite product structure. We then obtain a bireflective subcategory of [ Cop, Set] and deduce results relating its finite product structure with the monoidal structure of [ Cop, Set] determined by that of C . We also investigate closed structure. © 2000.

Type: Article
Title: Bireflectivity
DOI: 10.1016/S1571-0661(04)80011-2
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: http://discovery.ucl.ac.uk/id/eprint/1342361
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