[Anderson1992] Rings and Categories of Modules(有汉译)。本书是GTM系列的一本,适合已经有大学代数基础,希望进一步学习同调代数和范畴论的读者。本书联系了先修的线性代数、环和模理论,以及后继的更加抽象的范畴论。在学习范畴论过程中,如果感到缺乏实例的支持,可以回到本书中以具体的实例来理解。
以下列出若干拓扑学教程,特色都是以范畴化的方式讲解。
[May1999] A Concise Course in Algebraic Topology.
[Dieck2008] Algebraic Topology.
[Spanier1981] Alebraic Topology.
范畴论入门参考书籍:
[Harold Simmons2011] An Introduction to Category Theory
[Marco Grandis2018] Category Theory and Applications: A Textbook for Beginners
观点较为新的可参考:
[Spivak2014] Category Theory for the Sciences
[Riehl2016] Category theory in context
[KuśMarek2019] Category Theory in Physics, Mathematics, and Philosophy
参考论文
Maruyama Y. Category theory and foundations of life science: A structuralist perspective on cognition[J]. Biosystems, 2021, 203: 104376.
Riehl E, Verity D. Elements of∞-category theory[J]. Preprint available at www. math. jhu. edu/~ eriehl/elements.pdf, 2018.
Leinster T. Basic category theory[J]. arXiv preprint arXiv:1612.09375, 2016.
Smith P. Category theory: a gentle introduction[J]. 2016.
Linnebo Ø, Pettigrew R. Category theory as an autonomous foundation[J]. Philosophia Mathematica, 2011, 19(3): 227-254.
Blute R, Scott P. Category theory for linear logicians[J]. Linear logic in computer science, 2004, 316: 3-65.
Fuchs J, Schweigert C. Category theory for conformal boundary conditions[J]. Fields Institute Commun, 2003, 39: 25.
Feferman S. Categorical foundations and foundations of category theory[M]//Logic, foundations of mathematics, and computability theory. Springer, Dordrecht, 1977: 149-169.