Handbook of Categorical Algebra: Volume 2, Categories and StructuresThe Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence. The second, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibred categories. There is ample material here for a graduate course in category theory, and the book should also serve as a reference for users. |
Contents
2 | 7 |
Regular categories | 89 |
Algebraic theories | 122 |
5 | 138 |
8 | 146 |
10 | 166 |
11 | 173 |
12 | 179 |
6 | 231 |
7 | 237 |
8 | 251 |
3 | 260 |
4 | 266 |
5 | 272 |
Enriched category theory | 291 |
Topological categories | 349 |
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Handbook of Categorical Algebra: Volume 2, Categories and Structures Francis Borceux No preview available - 2008 |
Common terms and phrases
a-filtered colimits a-presentable abelian category abelian groups additive functor adjunction algebraic theory arrow axiom bidense bijections biproducts canonical cartesian functor cartesian morphism choose closure operation cocomplete cocone coequalizer Coker cokernel colim commutative compact composite cone consider diagram construction coproducts corresponding D₁ define definition elements equivalence relation exact sequence exists F preserves fibration fibration F fibre filtered colimits finite limits forgetful functor full subcategory functor F image factorization implies isomorphism Ker f kernel pair left adjoint Let F locally Mody monad monoidal closed category monomorphism morphism f natural transformation notation observe obvious phism preserves finite Proposition pseudo-elements pullback R-module regular cardinal regular category regular epimorphism remains to prove representable functor right adjoint small category subobjects subset suffices to prove symmetric monoidal closed T-algebras T-model theorem topology torsion theory unique morphism V-functor volume yields Yoneda lemma zero object