Related papers: On proper and exterior sequentiality

We establish a theory of complexes of relative correspondences. The theory generalizes the known theory of complexes of correspondences of smooth projective varieties. It will be applied in the sequel of this paper to the construction of…

A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.

We develop a theory of sheaves and cohomology on the category of proper modulus pairs. This complements [KMSY21], where a theory of sheaves and cohomology on the category of non-proper modulus pairs has been developed.

The notion of frontals in Euclidean space is introduced and the normal and tangent maps to frontals are studied for both geometrical and dynamical aspects of frontals. Moreover we observe that parallels of the tangent map to a frontal curve…

Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…

Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…

One fundamental consequence of a scheme $X$ being proper is that the functor classifying maps from $X$ to any other suitably nice scheme or algebraic stack is representable by an algebraic stack. This result has been generalized by…

We already saw in [A1] that the space of dynamically marked rational maps can be identified to a subspace of the space of covers between trees of spheres on which there is a notion of convergence that makes it sequentially compact. In the…

Recently discovered domain-specific formal systems -- specifically homotopy type theory and simplicial type theory -- provide new perspectives on spaces and categories in a natively equivalence-invariant setting. In this note, we expose…

For a finite dimensional vector space equipped with a $\mathbb C$-algebra structure, one can define rational maps using the algebraic structure. In this paper, we describe the growth of the degree sequences for this type of rational maps.

Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements &…

We develop category-theoretic framework for universal homogeneous objects, with some applications in the theory of Banach spaces, linear orderings, and in topology of compact spaces.

A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…

Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…

In this paper we will give a short and elementary proof that critical relations unfold transversally in the space of rational maps.

This paper is devoted to proving an infinite sequence of relations for rooted tree maps. On the way, we also give a basis for the space of rooted tree maps.

This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…

These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and not-so-typical applications to illustrate their use.

This paper gives a broad account of the various sequent-based proof formalisms in the proof-theoretic literature. We consider formalisms for various modal and tense logics, intuitionistic logic, conditional logics, and bunched logics. After…

Questions of set-theoretic size play an essential role in category theory, especially the distinction between sets and proper classes (or small sets and large sets). There are many different ways to formalize this, and which choice is made…