## 573 Citations

More Concise Algebraic Topology: Localization, Completion, and Model Categories

- Mathematics
- 2012

With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and…

From Categories to Homotopy Theory

- Mathematics
- 2020

Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous…

Foundations of Stable Homotopy Theory

- Mathematics
- 2020

The beginning graduate student in homotopy theory is confronted with a vast literature on spectra that is scattered across books, articles and decades. There is much folklore but very few easy entry…

Topic Proposal Algebraic K-Theory and the Additivity Theorem

- Mathematics
- 2010

Algebraic K-theory is the meeting ground for various other subjects such as algebraic geometry, number theory, and algebraic topology. We will try to expose some of these connections. Due to the…

Lectures on Algebraic Topology II

- Mathematics
- 2020

These notes represent my lectures in 18.906, the second half of a two-semester course on Algebraic Topology offered at MIT in spring 2020. I led both 18.905 and 18.906 in 2016–2017, and the record of…

Notes on Category Theory with examples from basic mathematics

- MathematicsArXiv
- 2019

These notes were originally developed as lecture notes for a category theory course. They should be well-suited to anyone that wants to learn category theory from scratch and has a scientific mind.…

WOMP 2006: ALGEBRAIC TOPOLOGY

- Mathematics
- 2006

One of the main goals of algebraic topology involves the transformation of topological properties into algebraic ones. In large part, this is accomplished by assigning suitable algebraic invariants…

A PRIMER ON SPECTRAL SEQUENCES Contents

- Mathematics
- 2009

This chapter contains those results about spectral sequences that we used earlier in the book, incorporated into a brief background compendium of the very minimum that anybody interested in algebraic…

Algebraic Topology 2.0

- Mathematics
- 2012

The efficiency of contemporary algebraic topology is not optimal since the category of topological spaces can be made more algebraic by introducing a profoundly new (-1)-dimensional topological space…

Unstable cohomology operations : computational aspects of plethories

- Mathematics
- 2017

Generalised cohomology theories are a broad class of powerful invariants in algebraic topology. Unstable cohomology operations are a useful piece of structure associated to a such a theory and as a…