This textbook provides an introduction to elementary category theory, with the aim of making this subject more accessible. The goal of this book is to present the five major ideas of category theory: categories, functors, natural transformations, universality, and adjoints. Thes…
From April 2009 until March 2016, the German Science Foundation supported generously the Priority Program SPP 1388 in Representation Theory. The core principles of the projects realized in the framework of the priority program have been categorification and geometrization, this …
![Elements of [infinity]-category theory](https://covers.openlibrary.org/b/isbn/9781108837989-M.jpg?default=false)
The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might…
This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first exa…
This paper offers a systematic approach to all mathematical theories with local/global behavior. To build objects with local and global aspects, on begins with a category of [script]C of allowed local structures, and somehow derives a category [script]C[superscript]gl of things …
At the heart of this short introduction to category theory is the idea of a universal property, important throughout mathematics. After an introductory chapter giving the basic definitions, separate chapters explain three ways of expressing universal properties: via adjoint func…
This English edition of Yuri I. Manin's well-received lecture notes provides a concise but extremely lucid exposition of the basics of algebraic geometry and sheaf theory. The lectures were originally held in Moscow in the late 1960s, and the corresponding preprints were widely …
