Exercices de style: a homotopy theory for set theory, I

Abstract

We construct a model category (in the sense of Quillen) for set theory, starting from two arbitrary, but natural, conventions. It is the simplest category satisfying our conventions and modelling the notions of finiteness, countability and infinite equi-cardinality. In a subsequent paper \cite{GaHa1} we give a homotopy theoretic dictionary of set theoretic concepts, most notably Shelah's covering number $\cov(λ, \aleph_1,\aleph_1,2)$, recovered from this model category. We argue that from the homotopy theoretic point of view our construction is essentially automatic following basic existing methods, and so is (almost all) the verification that the construction works.

References in corpus (4)

• A Primer for Black Hole Quantum Physics
• On the relation between Unruh and Sokolov--Ternov effects
• New Approach to Arakelov Geometry
• Taking the Temperature of a Black Hole

Cited by in corpus (61)

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• Quantum Gravity Effects in Geodesic Motion and Predictions of Equivalence Principle Violation
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• 4D scale-dependent Schwarzschild-AdS/dS black holes: study of shadow and weak deflection angle and greybody bounding
• Equivalence Principle for Quantum Systems: Dephasing and Phase Shift of Free-Falling Particles
• Hawking radiation from cubic and quartic black holes via tunneling of GUP corrected scalar and fermion particles
• Detecting Acceleration-Enhanced Vacuum Fluctuations with Atoms Inside a Cavity
• Analytical Solutions in a Cosmic String Born-Infeld-dilaton Black Hole Geometry: Quasinormal Modes and Quantization
• Shadow and greybody bounding of a regular scale-dependent black hole solution
• On the Universality of Hawking Radiation
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• New perspectives on Hawking radiation
• Entropic force approach to noncommutative Schwarzschild black holes signals a failure of current physical ideas
• Quasinormal modes and greybody factors of symmergent black hole
• Black hole kinematics: the "in"-vacuum energy density and flux for different observers
• Quantum Tunneling and Quasinormal Modes in the Spacetime of Alcubierre Warp Drive
• A Quantal Tolman Temperature
• Cavities in curved spacetimes: the response of particle detectors
• Equivalence principle and HBAR entropy of an atom falling into a quantum corrected black hole
• Hawking versus Unruh effects, or the difficulty of slowly crossing a black hole horizon
• Entropic force approach in a noncommutative charged black hole and the equivalence principle
• Violation of equivalence in an accelerating atom-mirror system in the generalized uncertainty principle framework
• Hawking, Fiducial, and Free-fall Temperatures of Black Hole on Gravity's Rainbow
• Equivalence principle violation at finite temperature in scalar-tensor gravity
• The Vaidya metric: expected and unexpected traits of evaporating black holes
• Near horizon aspects (and beyond) of acceleration radiation of an atom falling into a large class of static spherically symmetric black hole geometries
• Quantum free fall motion and quantum violation of weak equivalence principle
• An exact derivation of the Hawking effect in canonical formulation
• Origin of Hawking Radiation: Firewall or Atmosphere?
• A tensorial description of particle perception in black-hole physics
• Hawking radiation in the kappa-spacetime
• The Quantum Field Theory Boundaries Applicability and Black Holes Thermodynamics
• Gravitons to Photons -- attenuation of gravitational waves
• Uniformly accelerated detector in the $\kappa$-deformed Dirac vacuum
• Proper temperature of Schwarzschild AdS black hole revisited
• Effective Tolman temperature induced by trace anomaly
• Virtual transitions in an atom-mirror system in the presence of two scalar photons
• Quasinormal Modes and Greybody Factors of Charged Symmergent Black Hole
• Interaction between gravitational radiation and electromagnetic radiation
• Remarks on distinguishability of Schwarzschild spacetime and thermal Minkowski spacetime using Resonance Casimir-Polder interaction
• HBAR entropy of Infalling Atoms into a GUP-corrected Schwarzschild Black Hole and equivalence principle
• Cosmological Principle in Newtonian Dynamics
• The effective Tolman temperature in curved spacetimes
• Atom-field dynamics in curved spacetime
• Equivalence in virtual transitions between uniformly accelerated and static atoms: from a bird's eye
• Modified Hawking temperatures of black holes in Lorentz violation theory
• Unruh-DeWitt detector in presence of multiple scalar fields : A Toy Model
• Optical, Dynamic and Topological Characteristics of Deformed Schwarzschild Black Holes
• Thermality and athermality in the Unruh effect
• Excavations at the gravitationally collapsed site: Recent findings
• Non-Abelian Firewall
• Hawking Radiation -- Revisited
• Hawking effect of AdS${}_2$ black hole in the Jackiw-Teitelboim model
• Thermal radiation in curved spacetime using influence functional formalism
• Foundations as Superstructure. (Reflections of a practicing mathematician)
• The univalence axiom in posetal model categories
• Hawking and Unruh radiation perception by different observers: applications of the effective temperature function (in Spanish)
• Numerical homotopy continuation for control and online identification of nonlinear systems: the survey of selected results
• Black holes and their horizons in semiclassical and modified theories of gravity
• Is equivalence principle valid for quantum gravitational field?
• Relativistic Quantum Communication