Results 31 to 40 of about 9,831,323 (353)

String diagrams for Strictification and Coherence [PDF]

Logical Methods in Computer Science
Whereas string diagrams for strict monoidal categories are well understood, and have found application in several fields of Computer Science, graphical formalisms for non-strict monoidal categories are far less studied.
Paul Wilson, Dan Ghica, Fabio Zanasi
doaj   +1 more source

On the Axiomatic Systems of Steenrod Homology Theory of Compact Spaces [PDF]

, 2017
On the category of compact metric spaces an exact homology theory was defined and its relation to the Vietoris homology theory was studied by N. Steenrod [S].
Beridze, Anzor, Mdzinarishvili, Leonard
core   +3 more sources

Dirichlet Polynomials and Entropy

Entropy, 2021
A Dirichlet polynomial d in one variable y is a function of the form d(y)=anny+⋯+a22y+a11y+a00y for some n,a0,…,an∈N. We will show how to think of a Dirichlet polynomial as a set-theoretic bundle, and thus as an empirical distribution.
David I. Spivak, Timothy Hosgood
doaj   +1 more source

Who Needs Category Theory?

EPiC Series in Computing, 2020
In mathematical applications, category theory remains a contentious issue, with enthusiastic fans and a skepticalmajority. In a muted form this split applies to the authors ofthis note. When we learned that the only mathematically soundfoundation of topological quantum computing in the literature isbased on category theory, the skeptical author ...
Blass, Andreas, Gurevich, Yuri
openaire   +3 more sources

Waldhausen K-theory of spaces via comodules [PDF]

, 2016
Let $X$ be a simplicial set. We construct a novel adjunction between the categories of retractive spaces over $X$ and of $X_{+}$-comodules, then apply recent work on left-induced model category structures (arXiv:1401.3651v2 [math.AT],arXiv:1509.08154 ...
Hess, Kathryn, Shipley, Brooke
core   +3 more sources

THE MAGNITUDE OF A METRIC SPACE: FROM CATEGORY THEORY TO GEOMETRIC MEASURE THEORY [PDF]

, 2016
Magnitude is a numerical isometric invariant of metric spaces, whose definition arises from a precise analogy between categories and metric spaces. Despite this exotic provenance, magnitude turns out to encode many invariants from integral geometry and ...
T. Leinster, M. Meckes
semanticscholar   +1 more source

Mathematical Modelling by Help of Category Theory: Models and Relations between Them [PDF]

, 2021
Dmitrii Legatiuk
openalex   +3 more sources

Formalising Autonomous Construction Sites with the Help of Abstract Mathematics

Eng, 2023
With the rapid development of modern technologies, autonomous or robotic construction sites are becoming a new reality in civil engineering. Despite various potential benefits of the automation of construction sites, there is still a lack of ...
Dmitrii Legatiuk, Daniel Luckey
doaj   +1 more source

Decomposition theories for abelian categories [PDF]

Transactions of the American Mathematical Society, 1973
Both the classical approach to decomposition theories and Fisher’s technique of constructing decomposition theories from radical functions are extended to and exploited in the context of abelian categories. These two different approaches to decomposition theories for abelian categories intertwine in one theorem from which flows necessary and sufficient
Fisher, Joe W., Wolff, Harvey
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A Model of Directed Graph Cofiber

Axioms, 2022
In the homotopy theory of spaces, the image of a continuous map is contractible to a point in its cofiber. This property does not apply when we discretize spaces and continuous maps to directed graphs and their morphisms.
Zachary McGuirk, Byungdo Park
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