Seven Sketches in Compositionality: An Invitation to Applied Category Theory

Livro digital

Título:
Seven Sketches in Compositionality: An Invitation to Applied Category Theory

Autor:
Brendan Fong, David I. Spivak

Categoria:
Tecnologia > Geral

Doador:
Raffaello D. N.

Sinopse:
Category theory often feels like a language for distant abstractions, but this book opens with a very concrete promise: start from Chapter 1, “Generative effects: Orders and adjunctions,” and you quickly move from simple notions of order into the machinery that makes compositional thinking work across disciplines. The chapter-by-chapter structure is built to let readers see how structures and coherence interact, rather than treating the subject as a monolith. From there, the table of contents shows a carefully staged progression through the core ideas of the field, with chapters organized around motivating problems and the category-theoretic tools they require. The preface frames the journey through preorders, Galois connections, monoidal categories, profunctors, categorification, and related advanced topics, while also pointing to applications in circuits, control theory, cascade failures, information integration, and hybrid systems. The result is a compact but ambitious invitation to applied category theory. It suits readers who want both conceptual orientation and a genuine taste of the mathematics, including exercises, solutions, and a structure that encourages returning after each chapter. The book’s distinctive value is its bridge-building mindset: it connects abstract theory to real-world modeling while still respecting the internal coherence that makes the subject powerful.