Categories and Functors

Description

CONTENTS========Preface1. Preliminary Notions1.1 Definition of a Category1.2 Functors and Natural Transformations1.3 Representable Functors1.4 Duality1.5 Monomorphisms. Epimorphisms. and Isomorphisms1.6 Subobjects and Quotient Objects1.7 Zero Objects and Zero Morphisms1.8 Diagrams1.9 Difference Kernels and Difference Cokernels1.10 Sections and Retractions1.11 Products and Coproducts1.12 Intersections and Unions1.13 Images. Coimages. and Counterimages1.14 Multifunctors1.15 The Yoneda Lemma1.16 Categories as ClassesProblems2. Adjoint Functors and Limits2.1 Adjoint Functors2.2 Universal Problems2.3 Monads2.4 Reflexive Subcategories2.5 Limits and Colimits2.6 Special Limits and Colimits2.7 Diagram Categories2.8 Constructions with Limits2.9 The Adjoint Functor Theorem2.10 Generators and Cogenerators2.11 Special Casesof the Adjoint Functor Theorem2.12 Full and Faithful FunctorsProblems3. Universal Algebra3.1 Algebraic Theories3.2 Algebraic Categories3.3 Free Algebras3.4 Algebraic Functors3.5 Examples of Algebraic Theories and Functors3.6 Algebras in Arbitrary CategoriesProblems4. Abelian Categories4.1 Additive Categories4.2 Abelian Categories4.3 Exact Sequences4.4 Isomorphism Theorems4.5 The Jordan-Holder Theorem4.6 Additive Functors4.7 Grothendieck Categories4.8 The Krull.Remak.Schmidt.AzumayaTheorem4.9 Finitely Generated Objects4.10 Module Categories4.11 Semisimple and Simple Rings.12 Functor Categories4.13 Embedding TheoremsProblemsInjective and Projective Objects and HullsAppendix . Fundamentals of Set TheoryBibliographyIndex