3,516 research outputs found
Some insights on bicategories of fractions - III
We fix any bicategory together with a class of morphisms
, such that there is a bicategory of fractions
. Given another such pair
and any pseudofunctor
, we find necessary and
sufficient conditions in order to have an induced equivalence of bicategories
from to
. In particular, this gives
necessary and sufficient conditions in order to have an equivalence from any
bicategory of fractions to any
given bicategory .Comment: References updated, some misprints fixe
Photons uncertainty removes Einstein-Podolsky-Rosen paradox
Einstein, Podolsky and Rosen (EPR) argued that the quantum-mechanical
probabilistic description of physical reality had to be incomplete, in order to
avoid an instantaneous action between distant measurements. This suggested the
need for additional "hidden variables", allowing for the recovery of
determinism and locality, but such a solution has been disproved
experimentally. Here, I present an opposite solution, based on the greater
indeterminism of the modern quantum theory of Particle Physics, predicting that
the number of photons is always uncertain. No violation of locality is allowed
for the physical reality, and the theory can fulfill the EPR criterion of
completeness.Comment: 12 pages, 2 figure
Some insights on bicategories of fractions: representations and compositions of 2-morphisms
In this paper we investigate the construction of bicategories of fractions
originally described by D. Pronk: given any bicategory together
with a suitable class of morphisms , one can construct a bicategory
, where all the morphisms of are
turned into internal equivalences, and that is universal with respect to this
property. Most of the descriptions leading to this construction were long and
heavily based on the axiom of choice. In this paper we considerably simplify
the description of the equivalence relation on -morphisms and the
constructions of associators, vertical and horizontal compositions in
, thus proving that the axiom of choice is not
needed under certain conditions. The simplified description of associators and
compositions will also play a crucial role in two forthcoming papers about
pseudofunctors and equivalences between bicategories of fractions.Comment: Published in Theory and Applications of Categorie
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