title: Basic Category Theory (Cambridge Studies in Advanced Mathematics)
author:  Tom Leinster 
description: Assuming little mathematical background, this short introduction to category theory is ideal for beginning graduate students or advanced undergraduates learning category theory for the first time. Suitable for independent study or as a course book, it gives extensive explanations of the key concepts along with hundreds of examples and exercises.
zlib_text: Category Theory
  A Gentle Introduction
  Peter Smith
  University of Cambridge
  Version of February 8, 2016
  
  c⃝Peter Smith, 2016
  This PDF is an early incomplete version of work still very much in
  progress. For the latest and most complete version of this Gentle
  Introduction and for related materials see the Category Theory page
  at the Logic Matters website.
  Corrections, please, to ps218 at cam dot ac dot uk.
  
  Contents
  Preface
  ix
  0
  A very short introduction
  1
  0.1
  Why categories?
  1
  0.2
  What do you need to bring to the party?
  2
  0.3
  Theorems as exercises
  3
  0.4
  Notation and terminology
  3
  1
  Categories deﬁned
  4
  1.1
  The very idea of a category
  4
  1.2
  The category of sets
  6
  1.3
  More examples
  8
  1.4
  Diagrams
  13
  2
  Categories beget categories
  15
  2.1
  Duality
  15
  2.2
  Subcategories, product and quotient categories
  16
  2.3
  Arrow categories and slice categories
  18
  3
  Kinds of arrows
  22
  3.1
  Monomorphisms, epimorphisms
  22
  3.2
  Inverses
  24
  3.3
  Isomorphisms
  27
  3.4
  Isomorphic objects
  29
  4
  Initial and terminal objects
  3