Abstract and Concrete Categories: The Joy of Cats
by Jiri Adamek, Horst Herrlich, George Strecker
Publisher: John Wiley & Sons 1990
Number of pages: 496
A modern introduction to the theory of structures via the language of category theory. Unique to this book is the emphasis on concrete categories. Also noteworthy is the systematic treatment of factorization structures, which gives a new, unifying perspective to earlier work and summarizes recent developments. Each categorical notion is accompanied by many examples, usually moving from special cases to more general cases. Comprises seven chapters; the first five present the basic theory, while the last two contain more recent research results in the realm of concrete categories, cartesian closed categories and quasitopoi. The prerequisite is an elementary knowledge of set theory. Contains exercises.
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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 Marc Levine - American Mathematical Society
This book combines foundational constructions in the theory of motives and results relating motivic cohomology to more explicit constructions. Prerequisite for understanding the work is a basic background in algebraic geometry.
by Samson Abramsky, Nikos Tzevelekos - arXiv
These notes 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.
by Bartosz Milewski - unglue.it
Category theory is the kind of math that is particularly well suited for the minds of programmers. It deals with the kind of structure that makes programs composable. And I will argue strongly that composition is the essence of programming.