Related papers: Normalization and coherence for $\infty$-type theo…
We combine Homotopy Type Theory with axiomatic cohesion, expressing the latter internally with a version of "adjoint logic" in which the discretization and codiscretization modalities are characterized using a judgmental formalism of "crisp…
We define a notion of "theory of (1,infty)-categories", and we prove that such a theory is unique up to equivalence.
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…
We present a new kind of normalization theorem: linearization theorem for skew products. The normal form is a skew product again, with the fiber maps linear. It appears, that even in the smooth case, the conjugacy is only H\"older…
Promoting a theory with a finite number of terms into an effective field theory with an infinite number of terms worsens simplicity, predictability, falsifiability, and other attributes often favored in theory choice. However, the…
A natural procedure is introduced to replace the traditional, perturbatively generated counter terms to yield a formulation of covariant, self-interacting, nonrenormalizable scalar quantum field theories that has the added virtue of…
For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are…
In this paper we consider the notion of normality of sequences in shifts of finite type. A sequence is normal if the frequency of each block exists and is equal to the Parry measure of the block. We give a characterization of normality in…
The normal form theory for polynomial vector fields is extended to those for $C^\infty$ vector fields vanishing at the origin. Explicit formulas for the $C^\infty$ normal form and the near identity transformation which brings a vector field…
We introduce a procedure based on quantum expectation values of measurement observables to characterize quantum coherence. Our measure allows one to quantify coherence without having to perform tomography of the quantum state, and can be…
A categoricity theorem is established for patterns of resemblance of order 2 showing that the order in which patterns arise in a wide range of hierarchies is the same.
This is an introduction to the study of abstract homotopy theory by means of model categories and $(\infty,1)$-categories. The only prerequisites are very basic general topology and abstract algebra. None categorical background is needed.…
In physics we attempt to infer the rules governing a system given only the results of imprecise measurements. This is an ill-posed problem because certain features of the system's state cannot be resolved by the measurements. However, by…
Coherence is a defining property of quantum theory that accounts for quantum advantage in many quantum information tasks. Although many coherence quantifiers have been introduced in various contexts, the lack of efficient methods to…
For the special theory of relativity, the normalization problem is formulated as the question how observers in constant relative motion may reach an agreement on space and time scales. As the normalization problem does not receive a…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
Voevodsky's univalence axiom is often motivated as a realization of the equivalence principle; the idea that equivalent mathematical structures satisfy the same properties. Indeed, in Homotopy Type Theory, properties and structures can be…
The usual mathematical formalism of quantum field theory is non-rigorous because it contains divergences that can only be renormalized by non-rigorous mathematical methods. The purpose of this paper is to present a method of subtraction of…
This paper is the second in a series of two papers about generalizing Quillen's Theorem A to strict $\infty$-categories. In the first one, we presented a proof of this Theorem A of a simplicial nature, direct but somewhat ad hoc. In the…
It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…