Results 1 to 10 of about 4,438 (73)
Infinitesimal Structure of Singularities
Universe, 2017 Some important problems of general relativity, such as the quantisation of gravity or classical singularity problems, crucially depend on geometry on very small scales.
Michael Heller, Jerzy Król
doaj +1 more source
A Topos Foundation for Theories of Physics: I. Formal Languages for Physics [PDF]
, 2007 This paper is the first in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time ...
A. Döring +15 more
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Rewriting Abstract Structures: Materialization Explained Categorically [PDF]
, 2019 The paper develops an abstract (over-approximating) semantics for double-pushout rewriting of graphs and graph-like objects. The focus is on the so-called materialization of left-hand sides from abstract graphs, a central concept in previous work.
Corradini, Andrea +4 more
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Finitary Topos for Locally Finite, Causal and Quantal Vacuum Einstein Gravity
, 2005 Previous work on applications of Abstract Differential Geometry (ADG) to discrete Lorentzian quantum gravity is brought to its categorical climax by organizing the curved finitary spacetime sheaves of quantum causal sets involved therein, on which a ...
Raptis, Ioannis
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On choice rules in dependent type theory [PDF]
, 2017 In a dependent type theory satisfying the propositions as types correspondence together with the proofs-as-programs paradigm, the validity of the unique choice rule or even more of the choice rule says that the extraction of a computable witness from an ...
Maietti, MARIA EMILIA
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Topos theory and `neo-realist' quantum theory
, 2007 Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects.
A. Döring +20 more
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Topos Semantics for Higher-Order Modal Logic [PDF]
, 2014 We define the notion of a model of higher-order modal logic in an arbitrary elementary topos $\mathcal{E}$. In contrast to the well-known interpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the subobject ...
Awodey, Steve +2 more
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Higher Theory and the Three Problems of Physics [PDF]
, 2017 According to the Butterfield--Isham proposal, to understand quantum gravity we must revise the way we view the universe of mathematics. However, this paper demonstrates that the current elaborations of this programme neglect quantum interactions.
Veilahti, Antti
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Van Kampen Colimits and Path Uniqueness
, 2018 Fibred semantics is the foundation of the model-instance pattern of software engineering. Software models can often be formalized as objects of presheaf topoi, i.e, categories of objects that can be represented as algebras as well as coalgebras, e.g ...
König, Harald, Wolter, Uwe
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Characterizing Van Kampen Squares via Descent Data
, 2012 Categories in which cocones satisfy certain exactness conditions w.r.t. pullbacks are subject to current research activities in theoretical computer science.
A. Grothendieck +20 more
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