Category theory

[Papers and Books]

Ordinary category theory

• Emily Riehl. Category theory in context, 2014.

• Saunders Mac Lane. Categories for the working mathematician, 1978.

Extraordinary / Higher category theory

• Andre Joyal. The theory of quasi-categories I & II (in preparation)

• Andre Joyal. Quasi-categories and Kan complexes, 2002.

• Andre Joyal. The theory of quasi-categories and its applications, 2008.

• Jacob Lurie. Higher topos theory, 2012.

• Jacob Lurie. Higher algebra, 2017.

• Jacob Lurie. Kerodon, 2018.

• Jacob Lurie. Derived algebraic geometry I: Stable infinity categories, 2009.

• Jacob Lurie. Derived algebraic geometry II: Noncommutative algebra, 2007.

• Jacob Lurie. Derived algebraic geometry III: Commutative algebra, 2009. 

• Moritz Groth. A short course on infinity categories, 2015.

• Rune Haugseng. Yet another introduction to infinity categories, 2025.

• Markus Land. Introduction to infinity category, 2021.

Model category theory

• Mark Hovey. Model Categories, 1999.

• Emily Riehl. Categorical homotopy theory, 2014. 

• Scott Balchin. A handbook of model categories, 2021.

Triangulated category theory

• Amnon Neeman. Triangulated category, 2001.

• T. Holm-P. Jorjensen-R. Rouquier. Triangulated category, 2010.