Introduction to Categories and Categorical Logic
by Samson Abramsky, Nikos Tzevelekos
Publisher: arXiv 2011
Number of pages: 101
The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The main prerequisite is a basic familiarity with the elements of discrete mathematics: sets, relations and functions.
Home page url
Download or read it online for free here:
by Jacob Lurie - Princeton University Press
Jacob Lurie presents the foundations of higher category theory, using the language of weak Kan complexes, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
by Andrea Asperti, Giuseppe Longo - MIT Press
Here is an introduction to category theory for the working computer scientist. It is a self-contained introduction to general category theory and the mathematical structures that constitute the theoretical background.
by Pierre Schapira - UPMC
These notes introduce the language of categories and present the basic notions of homological algebra, first from an elementary point of view, next with a more sophisticated approach, with the introduction of triangulated and derived categories.
by Michael Barr, Charles Wells - Springer-Verlag
Introduction to toposes, triples and theories and the connections between them. The book starts with an introduction to category theory, then introduces each of the three topics of the title. Exercises provide examples or develop the theory further.