Handbook of Categorical Algebra 2: Categories and Structures

✍ Scribed by Francis Borceux

• Publisher: Cambridge University Press
• Year: 1994
• Tongue: English
• Leaves: 461
• Series: Encyclopedia of Mathematics and its Applications 51
• Category: Library

✦ Synopsis

The second volume, 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 fibered categories.

✦ Table of Contents

Cover......Page A001.djvu
Title page......Page all_11227_to_0066.cpc.djvu
Contents......Page all_11227_to_0066.cpc0005.djvu
Preface to volume 2......Page all_11227_to_0066.cpc0008.djvu
Introduction to this handbook......Page all_11227_to_0066.cpc0011.djvu
Contents of the three volumes......Page all_11227_to_0066.cpc0013.djvu
1.1 Zero objects and kernels......Page all_11227_to_0066.cpc0014.djvu
1.2 Additive categories and biproducts......Page all_11227_to_0066.cpc0016.djvu
1.3 Additive functors......Page all_11227_to_0066.cpc0021.djvu
1.4 Abelian categories......Page all_11227_to_0066.cpc0026.djvu
1.5 Exactness properties of abelian categories......Page all_11227_to_0066.cpc0029.djvu
1.6 Additivity of abelian categories......Page all_11227_to_0066.cpc0034.djvu
1.7 Union of subobjects......Page all_11227_to_0066.cpc0039.djvu
1.8 Exact sequences......Page all_11227_to_0066.cpc0045.djvu
1.9 Diagram chasing......Page all_11227_to_0066.cpc0047.djvu
1.10 Some diagram lemmas......Page all_11227_to_0066.cpc0053.djvu
1.11 Exact functors......Page all_11227_to_0066.cpc0062.djvu
1.12 Torsion theories......Page all_11227_to_0066.cpc0064.djvu
1.13 Localizations of abelian categories......Page all_11227_to_0132.cpc0009.djvu
1.14 The embedding theorem......Page all_11227_to_0132.cpc0018.djvu
1.15 Exercises......Page all_11227_to_0132.cpc0033.djvu
2.1 Exactness properties of regular categories......Page all_11227_to_0132.cpc0036.djvu
2.2 Definition in terms of strong epimorphisms......Page all_11227_to_0132.cpc0039.djvu
2.3 Exact sequences......Page all_11227_to_0132.cpc0042.djvu
2.4 Examples......Page all_11227_to_0132.cpc0045.djvu
2.5 Equivalence relations......Page all_11227_to_0132.cpc0048.djvu
2.6 Exact categories......Page all_11227_to_0132.cpc0052.djvu
2.7 An embedding theorem......Page all_11227_to_0132.cpc0057.djvu
2.8 The calculus of relations......Page all_11227_to_0132.cpc0060.djvu
2.9 Exercises......Page all_11227_to_0198.cpc.djvu
3.1 The theory of groups revisited......Page all_11227_to_0198.cpc0003.djvu
3.2 A glance at universal algebra......Page all_11227_to_0198.cpc0006.djvu
3.3 A categorical approach to universal algebra......Page all_11227_to_0198.cpc0011.djvu
3.4 Limits and colimits in algebraic categories......Page all_11227_to_0198.cpc0018.djvu
3.5 The exactness properties of algebraic categories......Page all_11227_to_0198.cpc0020.djvu
3.6 The algebraic lattices of subobjects......Page all_11227_to_0198.cpc0022.djvu
3.7 Algebraic functors......Page all_11227_to_0198.cpc0024.djvu
3.8 Freely generated models......Page all_11227_to_0198.cpc0027.djvu
3.9 Characterization of algebraic categories......Page all_11227_to_0198.cpc0039.djvu
3.10 Commutative theories......Page all_11227_to_0198.cpc0047.djvu
3.11 Tensor product of theories......Page all_11227_to_0198.cpc0054.djvu
3.12 A glance at Morita theory......Page all_11227_to_0198.cpc0060.djvu
3.13 Exercises......Page all_11227_to_0198.cpc0063.djvu
4 Monads......Page all_11227_to_0264.cpc.djvu
4.1 Monads and their algebras......Page all_11227_to_0264.cpc0003.djvu
4.2 Monads and adjunctions......Page all_11227_to_0264.cpc0008.djvu
4.3 Limits and colimits in categories of algebras......Page all_11227_to_0264.cpc0012.djvu
4.4 Characterization of monadic categories......Page all_11227_to_0264.cpc0027.djvu
4.5 The adjoint lifting theorem......Page all_11227_to_0264.cpc0036.djvu
4.6 Monads with rank......Page all_11227_to_0264.cpc0046.djvu
4.7 A glance at descent theory......Page all_11227_to_0264.cpc0052.djvu
4.8 Exercises......Page all_11227_to_0330.cpc.djvu
5 Accessible categories......Page all_11227_to_0330.cpc0003.djvu
5.1 Presentable objects in a category......Page all_11227_to_0330.cpc0004.djvu
5.2 Locally presentable categories......Page all_11227_to_0330.cpc0005.djvu
5.3 Accessible categories......Page all_11227_to_0330.cpc0012.djvu
5.4 Raising the degree of accessibility......Page all_11227_to_0330.cpc0016.djvu
5.5 Functors with rank......Page all_11227_to_0330.cpc0021.djvu
5.6 Sketches......Page all_11227_to_0330.cpc0026.djvu
5.7 Exercises......Page all_11227_to_0330.cpc0038.djvu
6 Enriched category theory......Page all_11227_to_0330.cpc0040.djvu
6.1 Symmetric monoidal closed categories......Page all_11227_to_0330.cpc0041.djvu
6.2 Enriched categories......Page all_11227_to_0330.cpc0049.djvu
6.3 The enriched Yoneda lemma......Page all_11227_to_0330.cpc0058.djvu
6.4 Change of base......Page all_11227_to_0330.cpc0062.djvu
6.5 Tensors and cotensors......Page all_11227_to_0396.cpc0003.djvu
6.6 Weighted limits......Page all_11227_to_0396.cpc0008.djvu
6.7 Enriched adjunctions......Page all_11227_to_0396.cpc0023.djvu
6.8 Exercises......Page all_11227_to_0396.cpc0030.djvu
7 Topological categories......Page all_11227_to_0396.cpc0032.djvu
7.1 Exponentiable spaces......Page all_11227_to_0396.cpc0033.djvu
7.2 Compactly generated spaces......Page all_11227_to_0396.cpc0042.djvu
7.3 Topological functors......Page all_11227_to_0396.cpc0049.djvu
7.4 Exercises......Page all_11227_to_0396.cpc0054.djvu
8 Fibred categories......Page all_11227_to_0396.cpc0056.djvu
8.1 Fibrations......Page all_11227_to_0396.cpc0057.djvu
8.2 Cartesian functors......Page all_11227_to_0396.cpc0065.djvu
8.3 Fibrations via pseudo-functors......Page all_11227_to_0456.cpc0004.djvu
8.4 Fibred adjunctions......Page all_11227_to_0456.cpc0011.djvu
8.5 Completeness of a fibration......Page all_11227_to_0456.cpc0016.djvu
8.6 Locally small fibrations......Page all_11227_to_0456.cpc0029.djvu
8.7 Definability......Page all_11227_to_0456.cpc0041.djvu
8.8 Exercises......Page all_11227_to_0456.cpc0049.djvu
Bibliography......Page all_11227_to_0456.cpc0053.djvu
Index......Page all_11227_to_0456.cpc0056.djvu