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TOPOS THEORY AND SPACETIME STRUCTURE
International Journal of Geometric Methods in Modern Physics, 2007According to the recently proposed model of spacetime, various difficulties of quantum field theories and semiclassical quantum gravity on curved 4-Minkowski spacetimes gain new formulations, leading to new solutions. The quantum mechanical effects appear naturally when diffeomorphisms are lifted to 2-morphisms between topoi.
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Unifying mathematics through topos theory
2023The paper "The unification of Mathematics via Topos Theory", written in 2010 and recently published in the book "Logic in Question. Studies in Universal Logic", introduced a set of principles and methodologies for unifying distinct mathematical theories with each other, resulting from a new view of Grothendieck toposes as “bridge” objects for ...
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2015
This chapter is a rapid introduction to the geometric flavour of topos theory that is used thoughout the book. A Grothendieck topology is a formal calculus of coverings which generalizes the algebra of open covers of a topological space, and can exist in much more generality.
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This chapter is a rapid introduction to the geometric flavour of topos theory that is used thoughout the book. A Grothendieck topology is a formal calculus of coverings which generalizes the algebra of open covers of a topological space, and can exist in much more generality.
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2019
Category theory is a framework for the investigation of mathematical form and structure in their most general manifestations. Central to it is the concept of structure-preserving map, or transformation. While the importance of this notion was long recognized in geometry (witness, for example, Klein’s Erlanger Programm of 1872), its pervasiveness in ...
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Category theory is a framework for the investigation of mathematical form and structure in their most general manifestations. Central to it is the concept of structure-preserving map, or transformation. While the importance of this notion was long recognized in geometry (witness, for example, Klein’s Erlanger Programm of 1872), its pervasiveness in ...
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Abductive Realism in Topos Theory
2016The foundation of Badiou’s ontological schema relies on the notion of a transcendental T. As emerged from the analysis in the last chapter, T is in fact best understood as a two-fold entity: It is used to measure the degree of identity of relations between objects in the world, and, on the other hand, is a structured system of relations by itself ...
Gianluca Caterina, Rocco Gangle
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2013
Consistent-history quantum theory was developed as an attempt to deal with closed systems in quantum mechanics. Such innovation is needed since the standard Copenhagen interpretation is incapable of describing the universe as a whole, since the existence of an external observer is required.
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Consistent-history quantum theory was developed as an attempt to deal with closed systems in quantum mechanics. Such innovation is needed since the standard Copenhagen interpretation is incapable of describing the universe as a whole, since the existence of an external observer is required.
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Logical quantization of topos theory
International Journal of Theoretical Physics, 1996This paper is apparently a continuation of the author's programme of `quantizing' the entire foundations of mathematics, in which he turns his attention to topos theory, and in particular to the construction of a classifying topos for the theory of rings, which he takes as his goal (though it is never made clear why the theory of rings should be ...
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Internalizing Objects in Topos Theory
2018In this chapter we will explain how to define categorical notions internally within a topos. This internal description of objects is needed to understand the covariant approach to topos quantum theory explained in the next chapter.
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