Indexed induction and coinduction, fibrationally.

This paper extends the fibrational approach to induction and coinduction pioneered by Hermida and Jacobs, and developed by the current authors, in two key directions. First, we present a sound coinduction rule for any data type arising as the final coalgebra of a functor, thus relaxing Hermida and Jacobs’ restriction to polynomial data types. For this we introduce the notion of a quotient category with equality (QCE), which both abstracts the standard notion of a fibration of relations constructed from a given fibration, and plays a role in the theory of coinduction dual to that of a comprehension category with unit (CCU) in the theory of induction. Second, we show that indexed inductive and coinductive types also admit sound induction and coinduction rules. Indexed data types often arise as initial algebras and final coalgebras of functors on slice categories, so our key technical results give sufficent conditions under which we can construct, from a CCU (QCE) U : E -> B, a fibration with base B/I that models indexing by I and is also a CCU (QCE)

A bifibrational reconstruction of Lawvere's presheaf hyperdoctrine

Combining insights from the study of type refinement systems and of monoidal closed chiralities, we show how to reconstruct Lawvere's hyperdoctrine of presheaves using a full and faithful embedding into a monoidal closed bifibration living now over the compact closed category of small categories and distributors. Besides revealing dualities which are not immediately apparent in the traditional presentation of the presheaf hyperdoctrine, this reconstruction leads us to an axiomatic treatment of directed equality predicates (modelled by hom presheaves), realizing a vision initially set out by Lawvere (1970). It also leads to a simple calculus of string diagrams (representing presheaves) that is highly reminiscent of C. S. Peirce's existential graphs for predicate logic, refining an earlier interpretation of existential graphs in terms of Boolean hyperdoctrines by Brady and Trimble. Finally, we illustrate how this work extends to a bifibrational setting a number of fundamental ideas of linear logic.Comment: Identical to the final version of the paper as appears in proceedings of LICS 2016, formatted for on-screen readin

Arthur Kaufmann: En la encrucijada de la filosofía jurídica alemana de la posguerra. [Reseña]

Reseña de: José Antonio SANTOS, Arthur Kaufmann: En la encrucijada de la filosofía jurídica alemana de la posguerra, Comares, Granada, 2008, 326 pp

Los nuevos leviatanes. Teoria de los sujetos colectivos. [Reseña]

Reseña de: Nicolás LÓPEZ CALERA, Los nuevos leviatanes. Teoria de los sujetos colectivos, Marcial Pons, Madrid, 2007, 150 pp

Kant y la guerra. Una revisión de la Paz Perpetua desde las preguntas actuales. [Reseña]

Reseña de: Francisco José CONTRERAS PELÁEZ, Kant y la guerra. Una revisión de la Paz Perpetua desde las preguntas actuales. Tirant lo blanch. Valencia, 2007, 310 pp

Fijación externa en las fracturas-luxaciones centrales de cadera: a propósito de 3 casos

Se presentan tres casos de fractura-luxación central de cadera tratados mediante estabilización y reducción progresiva con fijación externa. Las ventajas de este tratamiento con respecto al tratamiento conservador o quirúrgico son la estabilización inmediata y la sencillez de realización. Los resultados de fijación externa obtenidos en estos pacientes demuestran una rehabilitación y deambulación precoz e independiente. La recuperación clínica y funcional fue satisfactoria en dos casos. En otro caso, con mala reducción quirúrgica previa, el resultado fue pobre.Three cases of central fracture-dislocation of the hip treated by stabilization and progressive reduction by means of external fixation are presented. The advantages of this procedure over the conservative or even the surgical treatment are the early stabilization and the fact that the technique is a step-forward procedure. The results obtained in these patients with external fixation of the hip led to a good rehabilitation and to an early independent ambulation. The clinical and functional recovery of these patients was satisfactory in two cases. In other with previous failed open reduction the result was poor

Una salida a los conflictos entre el Tribunal de Estrasburgo y el Tribunal de Luxemburgo

La perspectiva de integración de los diferentes ordenamientos jurídicos en la protección de los derechos fundamentales en Europa exige que la Unión Europea se adhiera el CEDH con el fin de paliar las divergencias y tensiones entre tribunales europeos, así como de éstos con los nacionales. Asimismo quedará con ello definido el estándar mínimo de protección de los derechos fundamentales en el ámbito europeo, al que deberán someterse, de forma necesaria, no solamente los ordenamientos constitucionales sino, igualmente, el ordenamiento de la Unión Europea