Read about category theory | 6 Discussions | Page 1

  1. L

    A Structure preserved by strong equivalence of metrics?

    Let ##d_1## and ##d_2## be two metrics on the same set ##X##. We say that ##d_1## and ##d_2## are equivalent if the identity map from ##(X,d_1)## to ##(X,d_2)## and its inverse are continuous. We say that they’re uniformly equivalent if the identity map and its inverse are uniformly...
  2. Auto-Didact

    A Taxonomy of Theories in Theoretical Physics

    It goes without saying that theoretical physics has over the years become overrun with countless distinct - yet sometimes curiously very similar - theories, in some cases even dozens of directly competing theories. Within the foundations things can get far worse once we start to run into...
  3. pairofstrings

    I System to represent objects in Mathematics

    Hi. Usually, Computer Programmers use Flow Charts, Algorithms, or UML diagrams to build a great software or system. In the same manner, in Mathematics, what do Mathematicians use to build a great system that they want to build. Category Theory is at the highest level of abstraction; then...
  4. SrVishi

    Algebra Categories for the Working Mathematician

    Hello. I am about to start learning category theory. I keep hearing mixed opinions on the book Categories for the Working Mathematician, by Sanders MacLane (I am aware he is one of the founders of the theory). Some say it's a "must read", and others have called it "outdated." What would seem...
  5. N

    Understanding the Coproduct in Grp as a Universal Object

    Homework Statement Coproducts exist in Grp. This starts on page 71. of his Algebra. Homework Equations [/B] Allow me to present the proof in it's entirety, modified only where it's convenient or necessary for TeXing it. I've underlined areas where I have issues and bold bracketed off my...
  6. N

    [itex]\hom_A(-,N)[/itex]Functor Takes Coproducts to Products

    A couple of notes first: 1. \hom_{A}(-,N) is the left-exact functor I'm referring to; Lang gives an exercise in the section preceeding to show this. 2. This might be my own idiosyncrasy but I write TFDC to mean 'The following diagram commutes' 3. Titles are short, so I know that the hom-functor...