My Notes or Write-ups
An introduction to Simplicial Categories : These notes mainly supplements the introduction provided in Jardine – Simplicial Homotopy Theory while adding some nuances extracted from other pieces of literature.
Useful online Notes
Kerodon : A nice online resource relating to $\infty$-categories by Jacob Lurie
The Stacks project : An amazingly comprehensive book relating to Algebraic Geometry
nLab : A very nice repository that covers both introductory and advanced graduate level topics. And although some pages are quite lost in abstractions, it is still very useful.
Useful tools
Graphical user interface – tikzcd : Allows you to graphically draw tikz-cd diagrams.
Latex command finder – Detexify : Allows you to find the latex command for any symbol.
Recommended Readings
Handbook of model categories : Exactly what you’d expect. A very exhaustive account of the machinery of model categories. This book is not intended to learn the material. Most material and proofs are referenced rather than replicated. However, it is an excellent source to learn relevant or useful facts about model categories and specific model structures.
Handbook of homotopy theory : This is a nice account of various ongoing research in homotopy theoretical fields. The chapters are succinct, start with the fundamental definition, and quickly provide an overview up to current state of the art.
Emily – Categorical Homotopy Theory : This is quite an advanced book and generally assumes some adequate background in the content presented. Although the background knowledge is technically not necessary, it is still paradoxically essential to provide the desired ease in reading.
Emily – Category Theory in Context : This book will go a little more in depth than other other introductory books I have seen but the perspectives it provide are absolutely worth it.
Steven Roman – Advanced Linear Algebra : One of the best books I have seen written on Linear Algebra that provides newer perspective and a nice platform to jump into general Module Theory. The book is intended as a re-reading of Linear Algebra in a new light.
D.H. Fremlin – Measure Theory : This might be an “analysis” recommendation but the way it presented measure theory is, in all sense, as “algebraic” as possible. The best part about this book is its exercises. If you are really interested in some nice exercises, you must give this book a try.
Sydney A. Morris – Topology Without Tears : This is a really nice book if you want to be introduced to topology gently. Moreover, the book actually contains some “**” marked exercises which might be somewhat ‘tearful’. This makes it a very balanced book to read.