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.
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by Daniele Turi - University of Edinburgh
These notes were written for a course in category theory. The course was designed to be self-contained, drawing most of the examples from category theory itself. It was intended for post-graduate students in theoretical computer science.
by Sen Hu, Xuexing Lu, Yu Ye - arXiv
In this paper, we reveal the combinatorial nature of tensor calculus for strict tensor categories and show that there exists a monad which is described by the coarse-graining of graphs and characterizes the algebraic nature of tensor calculus.
by P. J. Higgins - Van Nostrand Reinhold
A self-contained account of the elementary theory of groupoids and some of its uses in group theory and topology. Category theory appears as a secondary topic whenever it is relevant to the main issue, and its treatment is by no means systematic.
by Jiri Adamek, Horst Herrlich, George Strecker - John Wiley & Sons
A modern introduction to the theory of structures via the language of category theory, the emphasis is on concrete categories. The first five chapters present the basic theory, while the last two contain more recent research results.