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Category theory and applications : a textbook for beginners

Author: Marco Grandis
Publisher: Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2018] ©2018
Edition/Format:   Print book : EnglishView all editions and formats
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Document Type: Book
All Authors / Contributors: Marco Grandis
ISBN: 9789813231061 9813231068
OCLC Number: 1004010161
Description: x, 294 pages : illustrations ; 24 cm
Contents: Machine generated contents note: 0.1.Categories --
0.2.Universal properties --
0.3.Diagrams in a category --
0.4.Functors --
0.5.Natural transformations and adjunctions --
0.6.A brief outline --
0.7.Classes of categories --
0.8.Our approach --
0.9.Literature --
0.10.Notation --
0.11.Acknowledgements --
1.Categories, functors and natural transformations --
1.1.Categories --
1.2.Monoids and preordered sets as categories --
1.3.Monomorphisms and epimorphisms --
1.4.Functors --
1.5.Natural transformations and equivalence of categories --
1.6.Categories of functors, representable functors --
1.7.A category of Galois connections --
1.8.Elementary categories of relations and partial mappings --
2.Limits and colimits --
2.1.Basic limits and colimits --
2.2.General limits and completeness --
2.3.Pullbacks and pushouts --
2.4.Subobjects and quotients, regular and strong --
2.5.Factorisation systems --
2.6.Inductive limits and filtered colimits --
2.7.Universal arrows and free objects Note continued: 2.8.*Other universals --
3.Adjunctions and monads --
3.1.Adjoint functors --
3.2.Properties of adjunctions --
3.3.Comma categories --
3.4.Monoidal categories and exponentials --
3.5.The Adjoint Functor Theorem --
3.6.Monads and algebras --
3.7.Exercises and complements on monads --
3.8.*Idempotent monads and idempotent adjunctions --
4.Applications in Algebra --
4.1.Free algebraic structures --
4.2.Regular and Barr-exact categories --
4.3.Varieties of algebras --
4.4.Limits and free algebras --
4.5.Relations for regular categories --
5.Applications in Topology and Algebraic Topology --
5.1.Adjoints and limits in Topology --
5.2.Cylinder, cocylinder and homotopies --
5.3.Simplicial sets --
5.4.Cubical sets --
5.5.Hints at Directed Algebraic Topology --
6.Applications in Homological Algebra --
6.1.Kernels and cokernels --
6.2.Categories of lattices in Homological Algebra --
6.3.Puppe-exact categories --
6.4.Additive and abelian categories Note continued: 6.5.Projective p-exact categories and projective spaces --
6.6.Relations and induction for p-exact categories --
7.Hints at higher dimensional category theory --
7.1.From categories to 2-categories and bicategories --
7.2.Double categories --
7.3.Enriched, internal and ordered categories --
7.4.*Double categories of lattices in Homological Algebra --
7.5.*Double categories of relations in Homological Algebra --
7.6.*Factorisation systems as pseudo algebras for 2-monads.
Responsibility: Marco Grandis (Università di Genova, Italy).

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