Quotients of d-Frames


It is shown that every d-frame admits a complete lattice of quotients. Quotienting may be triggered by a binary relation on one of the two constituent frames, or by changes to the consistency or totality structure, but as these are linked by the reasonableness conditions of d-frames, the result in general will be that both frames are factored and both consistency and totality are increased.

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The results reported in this paper were obtained in Spring 2017, during visits by the third author to Birmingham and the first two authors to Prague. We gratefully acknowledge the hospitality and financial support extended to us by our two universities. The work was supported by the Grant SVV–2017–260452 and by the CE-ITI Grant, GAČR P202/12/G061. We are also grateful to the anonymous referee for spotting several hidden typos.

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Correspondence to Tomáš Jakl.

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Communicated by Jorge Picado.

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Jakl, T., Jung, A. & Pultr, A. Quotients of d-Frames. Appl Categor Struct 27, 261–275 (2019). https://doi.org/10.1007/s10485-018-09553-7

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  • Quotient
  • d-Frame
  • (Quasi)-congruence
  • Factorization system