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Maths › 00. General Mathematics ›

05.3 Categorical Abstraction

5.3 Categorical Abstraction Categorical abstraction studies objects through their relationships. Instead of asking only what an object contains, it asks how the object maps to and from other objects. This shift is important. At the algebraic level, we focus on operations inside a structure. At the categorical level, we focus on morphisms between structures and on how those morphisms compose. A category has objects and morphisms. If $$ f :...

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18. Category Theory; Homological Algebra

This volume develops category theory as a unifying language and homological algebra as a computational framework for algebraic structures. It connects algebra, topology, geometry, and logic through morphisms and functorial methods. Part I. Category Theory Foundations Chapter 1. Categories 1.1 Objects and morphisms 1.2 Composition and identities 1.3 Examples: sets, groups, spaces 1.4 Opposite categories 1.5 Basic constructions Chapter 2. Functors 2.1 Covariant and contravariant functors 2.2 Examples and constructions...