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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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Logical quantization of topos theory
International Journal of Theoretical Physics, 1996Traditionally set theory lies at the hub of all mathematics in the sense that every branch of mathematics, ranging from algebraic geometry to functional analysis, is to be considered as developed within some formal system of set theory. Recently topos theory, which is a natural generalization of set theory, has provided an alternative foundation of ...
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A survey of Fuzzy Sets and topos theory
Fuzzy Sets and Systems, 1991Abstract This paper is a comparison and contrast of approaches to many-valued mathematics offered by Fuzzy Set Theory and topos theory. It gives a survey of the categorical foundations of Fuzzy Set theory and related topoi. Topoi are not a basis for Fuzzy Set theory butthey do suggest appropriate directions to go and questions to ask for a synthesis ...
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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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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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The Uses and Abuses of the History of Topos Theory
The British Journal for the Philosophy of Science, 1990AbstractThe view that toposes originated as generalized set theory is a figment of set theoretically educated common sense.
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Probabilities in Topos Quantum Theory
2013The main idea in the topos formulation of quantum theory it to have logic as a fundamental concept and try and derive other concepts in terms of it. This is what is done in the case of probabilities.
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Entropy and Order: A Duality in Topos Theory
In the last decades, the theory of Categories introduced deep changes in the way math and physics are conceived, introducing new objects, theorems and laws. This sort work introduces an innovative theorem, which investigates the duality between entropy and order within the framework of a topos, a fundamental concept in category theory.openaire +1 more source