An Introduction to Category Theory in Four Easy Movements
by A. Schalk, H. Simmons
Publisher: Manchester University 2005
Number of pages: 197
Notes for a course offered as part of the MSc. in Mathematical Logic, Manchester University. From the table of contents: Development and exercises; Functors and natural transformations; Limits and colimits, a universal solution; Cartesian closed categories.
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by Paul Goerss, Kristen Schemmerhorn - Northwestern University
There are many ways to present model categories, each with a different point of view. Here we would like to treat model categories as a way to build and control resolutions. We are going to emphasize the analog of projective resolutions.
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 Mikael Vejdemo-Johansson - University of St. Andrews
An introduction to category theory that ties into Haskell and functional programming as a source of applications. Topics: definition of categories, special objects and morphisms, functors, natural transformation, (co-)limits and special cases, etc.
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.