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Notes on Category Theory with examples from basic mathematics
arXiv.org, 2019 These notes were originally developed as lecture notes for a category theory course. They should be well-suited to anyone that wants to learn category theory from scratch and has a scientific mind. There is no need to know advanced mathematics, nor any of the disciplines where category theory is traditionally applied, such as algebraic geometry or ...
Paolo Perrone
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Mathematical Modelling by Help of Category Theory: Models and Relations between Them [PDF]
Mathematics, 2021 The growing complexity of modern practical problems puts high demand on mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice is becoming particularly important. Methods for model comparison and model choice typically used in practical applications nowadays are
Dmitrii Legatiuk
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Rethinking equality in mathematics education with category theory [PDF]
The Mathematics EnthusiastTo provide an alternative to the flattening operations of equality, which are prevalent not only in mathematics but also in our everyday world, I introduce the relational structures of category theory and their more nuanced notions of equivalence ...
Kelly Paton
core +4 more sources
Interfacing biology, category theory and mathematical statistics [PDF]
Electronic Proceedings in Theoretical Computer Science, 2020 Motivated by the concept of degeneracy in biology (Edelman, Gally 2001), we establish a first connection between the Multiplicity Principle (Ehresmann, Vanbremeersch 2007) and mathematical statistics. Specifically, we exhibit two families of statistical tests that satisfy this principle to achieve the detection of a signal in noise.
Pastor, Dominique +3 more
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Mathematical Category Theory and Mathematical Philosophy [PDF]
, 2003 Explicit concepts and sufficiently precise definitions are the basis for further advance of a science beyond a given level. To move toward a situation where the whole population has access to the authentic results of science (italics mine) requires making explicit some general philosophical principles which can help to guide the learning, development ...
F. William Lawvere
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Reformalizing the notion of autonomy as closure through category theory as an arrow-first mathematics [PDF]
The 2023 Conference on Artificial Life, 2023 Life continuously changes its own components and states at each moment through interaction with the external world, while maintaining its own individuality in a cyclical manner. Such a property, known as "autonomy," has been formulated using the mathematical concept of "closure." We introduce a branch of mathematics called "category theory" as an ...
Hirota, Ryuzo +2 more
+6 more sources
Mathematical Morphology via Category Theory
, 2020 Mathematical morphology contributes many profitable tools to image processing area. Some of these methods considered to be basic but the most important fundamental of data processing in many various applications. In this paper, we modify the fundamental of morphological operations such as dilation and erosion making use of limit and co-limit preserving
Sharifipour, Hossein Memarzadeh +1 more
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Introduction to gestural similarity in music. An application of category theory to the orchestra [PDF]
, 2018 Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of music itself in terms of compositional structures and ...
Maria Mannone
semanticscholar +3 more sources
Tensor categories and the mathematics of rational and logarithmic conformal field theory [PDF]
Journal of Physics A: Mathematical and Theoretical, 2013 In response to the referees' helpful comments, further discussion of several issues is added, including in particular rigidity. Much of the paper is devoted to explaining what has been mathematically proved and where people can find these proofs. Several references added. 27 pages. Invited review article for publication in a special issue of J. Phys. A
Yi-Zhi Huang, James Lepowsky
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Philosophical Sketches on Category Theory Applied to Music-Mathematical Polar Semiotics
MusMat: Brazilian Journal of Music and Mathematics, 2020 This is an attempt to combine Matthai philosophy (of Heraclitan inspiration) and Category Theory using the Yoneda Lemma as a means for harmonizing the traditionally opposite values and conceptions dissociated between the Euclidean tradition and Heraclitus thought.
Gabriel Pareyón
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