Observations on category theory

Axiomathes 12 (1-2):151-155 (2001)
is a presentation of mathematics in terms of the fundamental concepts of transformation, and composition of transformations. While the importance of these concepts had long been recognized in algebra (for example, by Galois through the idea of a group of permutations) and in geometry (for example, by Klein in his Erlanger Programm), the truly universal role they play in mathematics did not really begin to be appreciated until the rise of abstract algebra in the 1930s. In abstract algebra the idea of transformation of structure (homomorphism) was central from the beginning, and it soon became apparent to algebraists that its most important concepts and constructions were in fact formulable in terms of that idea alone. Thus emerged the view that the essence of a mathematical structure is to be sought not in its internal constitution, but rather in the nature of its relationships with other structures of the same kind, as manifested through the network of transformations. This idea has achieved its fullest expression in category theory, an axiomatic framework within which the notions of transformation (as morphism or arrow) and composition (and also structure, as object) are fundamental, that is, are not defined in terms of anything else.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,351
External links
  •   Try with proxy.
  •   Try with proxy.
  • Through your library Configure
    References found in this work BETA

    No references found.

    Citations of this work BETA

    No citations found.

    Similar books and articles

    Monthly downloads

    Added to index


    Total downloads

    43 ( #32,902 of 1,088,372 )

    Recent downloads (6 months)

    1 ( #69,449 of 1,088,372 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature

    Start a new thread
    There  are no threads in this forum
    Nothing in this forum yet.