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ぱらぱらめくる『Category Theory』by Steve Awodey

ぱらぱらめくるシリーズ 圏論

Category Theory (Oxford Logic Guides)

Category Theory (Oxford Logic Guides)

  • ぱらぱらめくれるだろうか、と、思うが…
  • 目次
  • 1. Categories
    • 1.1 Introduction
    • 1.2 Functions of sets
    • 1.3 Definition of a category
    • 1.4 Examples of categories
    • 1.5 Isomorphisms
    • 1.6 Constructions on categories
    • 1.7 Free categories
    • 1.8 Foundations: large, small, and locally small
    • 1.9 Exercises
  • 2. Abstract structures
    • 2.1 Epis and monos
    • 2.2 Initial and terminal objects
    • 2.3 Generalized elements
    • 2.4 Products
    • 2.5 Examples of products
    • 2.6 Categories with products
    • 2.7 Hom-sets
    • 2.8 Exercises
  • 3. Duality
    • 3.1 The duality principle
    • 3.2 Coproducts
    • 3.3 Equalizers
    • 3.4 Coequalizers
    • 3.5 Exercises
  • 4. Groups and categories
    • 4.1 Groups in a category
    • 4.2 The category of groups
    • 4.3 Groups as categories
    • 4.4 Finitely presented categories
    • 4.5 Exercises
  • 5. Limits and colimits
    • 5.1 Subobjects
    • 5.2 Pullbacks
    • 5.3 Properties of pullbacks
    • 5.4 Limits
    • 5.5 Preservation of limits
    • 5.6 Colimits
    • 5.7 Exercises
  • 6. Exponentials
    • 6.1 Exponential in a category
    • 6.2 Cartesian closed categories
    • 6.3 Heyting algebras
    • 6.4 Propositional calculus
    • 6.5 Equational definition of CCC
    • 6.6 \lambda-calculus
    • 6.7 Variable sets
    • 6.8 Exercises
  • 7. Naturality
    • 7.1 Category of categories
    • 7.2 Representable structure
    • 7.3 Stone duality
    • 7.4 Naturality
    • 7.5 Examples of natural transformations
    • 7.7 Functor categories
    • 7.8 Monoidal categories
    • 7.9 Equivalence of categories
    • 7.11 Exercises
  • 8. Categories of diagrams
    • 8.1 Set-valued functor categories
    • 8.2 The Yoneda embedding
    • 8.3 The Yoneda lemma
    • 8.4 Applications of the Yoneda lemma
    • 8.5 Limits in categories of diagrams
    • 8.6 Colimits in categories of diagrams
    • 8.7 Exponentials in categoires of diagrams
    • 8.8 Topoi
    • 8.9 Exercises
  • 9. Adjoints
    • 9.1 Preliminary definition
    • 9.2 Hom-set definition
    • 9.3 Examples of adjoints
    • 9.4 Order adoints
    • 9.5 Quantifiers as adjoints
    • 9.6 RAPL
    • 9.7 Locally cartesian closed categories
    • 9.8 Adjoint functor theorem
    • 9.9 Exercises
  • 10. Modads and algebras
    • 10.1 The triangle identities
    • 10.2 Monads and adjoints
    • 10.3 Algebras for a monad
    • 10.4 Comonads and coalgebras
    • 10.5 Algebras for endofunctors
    • 10.6 Exercises