Related papers: High-level methods for homotopy construction in as…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…
Category theory provides a compact method of encoding mathematical structures in a uniform way, thereby enabling the use of general theorems on, for example, equivalence and universal constructions. In this article we develop the method of…
In this work we use Hodge theoretic methods to study homotopy types of complex projective manifolds with arbitrary fundamental groups. The main tool we use is the \textit{schematization functor} $X \mapsto (X\otimes \mathbb{C})^{sch}$,…
Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results…
This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…
Invertibility is an important concept in category theory. In higher category theory, it becomes less obvious what the correct notion of invertibility is, as extra coherence conditions can become necessary for invertible structures to have…
The subject logic in computer science should entail proof theoretic applications. So the question arises whether open problems in computational complexity can be solved by advanced proof theoretic techniques. In particular, consider the…
Actions of monoidal categories on categories, also known as actegories, have been familiar to category theorists for a long time, and yet a comprehensive overview of this topic seems to be missing from the literature. Recently, actegories…
We give a systematic approach to constructing non-reduced, locally Cohen-Macaulay schemes with reduced support a smooth projective variety. The hierarchy of such structures includes a lot of information about the underlying variety, its…
Constructing complex computation from simpler building blocks is a defining problem of computer science. In algebraic automata theory, we represent computing devices as semigroups. Accordingly, we use mathematical tools like products and…
A simplicial complex is a set equipped with a down-closed family of distinguished finite subsets. This structure, usually viewed as codifying a triangulated space, is used here directly, to describe "spaces" whose geometric realisation can…
Polygraphs are a higher-dimensional generalization of the notion of directed graph. Based on those as unifying concept, this monograph on polygraphs revisits the theory of rewriting in the context of strict higher categories, adopting the…
The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and…
We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only…
Consider the following Online Boolean Matrix-Vector Multiplication problem: We are given an $n\times n$ matrix $M$ and will receive $n$ column-vectors of size $n$, denoted by $v_1,\ldots,v_n$, one by one. After seeing each vector $v_i$, we…
Program reductions are used widely to simplify reasoning about the correctness of concurrent and distributed programs. In this paper, we propose a general approach to proof simplification of concurrent programs based on exploring generic…
This paper is the first step in a general program for defining cocalculus towers of functors via sequences of compatible monads. Goodwillie's calculus of homotopy functors inspired many new functor calculi in a wide range of contexts in…
Graphs are a fundamental abstraction in computer science and discrete mathematics, where information is encoded in their combinatorial structure. Graph-reduction techniques aim at simplifying graphs while preserving selected structural…
Homotopy type theory is a new branch of mathematics, based on a recently discovered connection between homotopy theory and type theory, which brings new ideas into the very foundation of mathematics. On the one hand, Voevodsky's subtle and…
This paper continues investigations in "synthetic homotopy theory": the use of homotopy type theory to give machine-checked proofs of constructions from homotopy theory We present a mechanized proof of the Blakers-Massey connectivity…