범주론

수학노트
둘러보기로 가기 검색하러 가기

노트

  • At a first glance category theory provides a unifying language among all the different areas of mathematics.[1]
  • The book explains category theory by examples and exercises rather than focusing on theorems and proofs.[2]
  • Category theory looks at mathematics on a large scale: objects and the relations between them, in the abstract.[3]
  • Much of modern mathematics is, literally, near-unthinkable without the organizing principles of category theory.[3]
  • The aim of this paper is to clarify the role of category theory in the foundations of mathematics.[4]
  • We end up on a more speculative note by examining the relationships between category theory and set theory.[4]
  • The objects studied in category theory are called categories.[5]
  • Category theory has provided the foundations for many of the twentieth century's greatest advances in pure mathematics.[6]
  • Category theory brings together many areas of pure mathematics (and also has close links to logic and to computer science).[7]
  • is a series of blog posts that gives a very clear walkthrough the basics on Category Theory.[8]
  • Categories for the Working Mathematician is commonly referred to as the “definitive” book on Category Theory.[8]
  • Written by one of the founders, it has a vast array of advancements that has been made since Category Theory was created.[8]
  • Category Theory in Context is fantastic, recent book written by one the world’s leading mathematicians in Category Theory: Emily Riehl.[8]
  • that helped me to discern more carefully the links between Category Theory and Quantum Computing.[9]
  • Category theory serves several purposes.[10]
  • Less superficially, category theory encourages a shift in attention to what structure is.[10]
  • In category theory the particular inner workings of an object do not matter at all.[10]
  • Still along the same theme, category theory allows to make precise the meaning of a certain construction being natural.[10]
  • Beginning postgraduate mathematicians will find this book an excellent introduction to all of the basics of category theory.[11]
  • In the last two decades, a new branch of category theory has developed – higher category theory.[12]
  • The work has been supported by an EU grant and by the Centre for Australian Category Theory at Macquarie University.[12]
  • In fact, this is precisely how category theory came to be.[13]
  • The mathematics of category theory formalises this unification.[13]
  • And these days it’s especially hard to escape the pervasiveness of category theory throughout modern mathematics.[13]
  • The narratives category theorists tell themselves Category theory is an attempt to provide general tools for all of mathematics.[14]
  • who does research in/looks to use the tools of category theory.[14]
  • Category theory takes a bird’s eye view of mathematics.[14]
  • The subject of this moderated mailing list is category theory.[15]
  • Summer School on selected topics in category theory and in algebraic topology, September 11-13, 2014, EPFL in Lausanne, Switzerland.[15]
  • The conference topics include algebraic topology, category theory, commutative algebra, differential geometry, and statistics.[15]
  • The conference topics include category theory, algebraic topology, and applied mathematics.[15]
  • Category theory can be very useful, but you don’t use it the same way you use other kinds of math.[16]
  • Categorical thinking may be more useful than category theory per se.[16]
  • After the patterns are found, the category theory may go way.[16]
  • After several cycles of fascination and frustration, I decided to dig into category theory.[16]
  • It gives an introduction to category theory assuming only minimal knowledge in set theory, algebra or topology.[17]
  • He's also done important work regarding the foundations of databases and schema, and it uses non-trivial results from category theory.[18]
  • in case it helps others who need examples of category theory.[18]
  • Category theory also provides a language for experimental design patterns, introducing formality while remaining flexible.[18]
  • Example stolen from Spivak: Category theory can serve as a mathematical model for mathematical modeling.[18]
  • This course introduces the basic notions of category theory: adjunction, natural transformation, functor and category.[19]
  • I doubt that a mathematical illiterate after reading the book will be able to tell you what category theory really is.[20]
  • Do not expect that after reading the book you will be ready to start reading current research in category theory.[20]
  • …notion of structure developed within category theory.[21]
  • you might guess that I've had category theory on my mind.[22]
  • --I thought it would be nice to tell you what category theory is in the grand scheme of (mathematical) things.[22]
  • " You'll notice that the "coast of category theory" is located in the lower right corner.[22]
  • The bridges between realms are also provided by category theory.[22]
  • The language of category theory has been used to formalize concepts of other high-level abstractions such as sets, rings, and groups.[23]
  • Several terms used in category theory, including the term "morphism", are used differently from their uses in the rest of mathematics.[23]
  • Many areas of mathematics can be formalised by category theory as categories.[23]
  • Using the language of category theory, many areas of mathematical study can be categorized.[23]
  • The basic trinity of concepts Category theory reflects on itself.[24]
  • This trinity of concepts category functor natural transformation is what category theory is built on.[24]
  • A major driving force behind the development of category theory is its ability to abstract and unify concepts.[24]
  • This abstraction power of category theory has led Norman Steenrod to coin the term abstract nonsense or general abstract nonsense for it.[24]
  • Riehl and Verity hope to move infinity category theory forward in another way as well.[25]
  • They’re specifying aspects of infinity category theory that work regardless of the model you’re in.[25]
  • As category theory is still evolving, its functions are correspondingly developing, expanding and multiplying.[26]
  • This is the definition one finds in most textbooks of category theory.[26]
  • These examples nicely illustrates how category theory treats the notion of structure in a uniform manner.[26]
  • Category theory unifies mathematical structures in two different ways.[26]

소스

  1. ↑ Department of Mathematics
  2. ↑ Category Theory for the Sciences
  3. ↑ 3.0 3.1 Category Theory
  4. ↑ 4.0 4.1 Category theory and the foundations of mathematics: Philosophical excavations
  5. ↑ Category Theory -- from Wolfram MathWorld
  6. ↑ Emily Riehl
  7. ↑ C2.7 Category Theory (2019-2020)
  8. ↑ 8.0 8.1 8.2 8.3 Category Theory: The Math Behind Mathematics
  9. ↑ Category Theory - the bedrock of mathematics ?
  10. ↑ 10.0 10.1 10.2 10.3 What is category theory useful for?
  11. ↑ Introduction category theory
  12. ↑ 12.0 12.1 Groundbreaking new approach to mathematical theory
  13. ↑ 13.0 13.1 13.2 An invitation to category theory
  14. ↑ 14.0 14.1 14.2 The n-Category Café
  15. ↑ 15.0 15.1 15.2 15.3 Categories Home Page
  16. ↑ 16.0 16.1 16.2 16.3 Apply category theory to modeling and software development
  17. ↑ SSPM 01
  18. ↑ 18.0 18.1 18.2 18.3 Most striking applications of category theory?
  19. ↑ Department of Computer Science and Technology
  20. ↑ 20.0 20.1 Cakes, Custard + Category Theory
  21. ↑ Category theory | mathematics
  22. ↑ 22.0 22.1 22.2 22.3 What is Category Theory Anyway?
  23. ↑ 23.0 23.1 23.2 23.3 Category theory
  24. ↑ 24.0 24.1 24.2 24.3 category theory in nLab
  25. ↑ 25.0 25.1 Quanta Magazine
  26. ↑ 26.0 26.1 26.2 26.3 Category Theory (Stanford Encyclopedia of Philosophy)

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'category'}, {'LEMMA': 'theory'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=범주론&oldid=51508"