Skip to main content Accessibility help
×
  1. Home
  2. Publications
  3. Textbooks
  4. Content Listing

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

36886 results in Cambridge Textbooks

Page 1635 of 1845

  • Part I - The category of sets

  • F. William Lawvere, State University of New York, Buffalo, Stephen H. Schanuel, State University of New York, Buffalo
  • Book:
    Conceptual Mathematics
    Published online:
    05 June 2012
    Print publication:
    30 July 2009, pp 11-12

  • Summary

    A map of sets is a process for getting from one set to another. We investigate the composition of maps (following one process by a second process), and find that the algebra of composition of maps resembles the algebra of multiplication of numbers, but its interpretation is much richer.

  • APPENDICES

  • F. William Lawvere, State University of New York, Buffalo, Stephen H. Schanuel, State University of New York, Buffalo
  • Book:
    Conceptual Mathematics
    Published online:
    05 June 2012
    Print publication:
    30 July 2009, pp 368-368

  • Summary

    The goal of this book has been to show how the notion of composition of maps leads to the most natural account of the fundamental notions of mathematics, from multiplication, addition, and exponentiation, through the basic notions of logic and of connectivity.

    Your further work with mathematics may apply it to physics, computer science or to other fields. In each of these, illuminating guides to the formulation and solution of problems often come from explicit recognition of structures occurring in commutative algebra, functional analysis, algebraic topology, etcetera. Clarifying unification of these branches has been developed during the last 60 years, using the categorical methods that you have begun to learn. To begin to deepen your knowledge of categories, here are four appendices which, although too brief for learning the subjects thoroughly, outline some important connections, in formulations which you will recognize in your subsequent encounters with mathematical topics.

    Appendix I A general description of the geometry of figures in a space and the algebra of functions on a space, together with their basic functorial behavior.

    Appendix II The description of Adjoint Functors and how they are exemplified in the categories of directed graphs and dynamical systems.

    Appendix III A very brief history of the emergence of the theory of categories from within various mathematical subjects.

    Appendix IV An annotated bibliography to guide you through elementary texts, monographs, and historical sources.

    May you enjoy the fruits of your perseverance.

Page 1635 of 1845