An Introduction to Homological Algebra

By Tomi Pannila. 2016

1,127 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics, Philosophy

View Paper: https://www.semanticscholar.org/paper/5c1f0774a801d6f6757430418b3a2e966e7d4f67

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Lorenzo Raspollini
2. Thomas Church
3. Martin Wolf
4. Lek-Heng Lim
5. Hongxing Chen
6. S. Shankar
7. Jordan S. Ellenberg
8. Changchang Xi

In Mathematical Physics

1. Jordan S. Ellenberg
2. Thomas Church
3. Lorenzo Raspollini
4. Martin Wolf
5. Lek-Heng Lim
6. Hongxing Chen
7. S. Shankar
8. Changchang Xi

In Philosophy

1. Thomas Church
2. Lek-Heng Lim
3. Hongxing Chen
4. S. Shankar
5. Jordan S. Ellenberg
6. Changchang Xi

Citations in the corpus

• Quantum link homology via trace functor I (2016, neutral): “For an introduction to homological algebra and derived categories see [Wei95].”
• Wasserstein Stability for Persistence Diagrams (2020, neutral): “These are based on standard constructions [43] and their properties.”
• Group Theory (2019, methodology): “We omit the proof, which can be found in [12], Theorem 6.”
• Good tilting modules and recollements of derived module categories (2010, background): “In the following, we shall recall some definitions and basic facts about derived functors (see [33, 23]).”
• Introduction to representation theory (2009, neutral): ““[W]hat gave me a Place among the Mathematicians of our Day, despite my Lack of Knowledge and Form, was the Audacity of my Thinking” [56, p.”
• L∞‐Algebras of Classical Field Theories and the Batalin–Vilkovisky Formalism (2018, background): “e tensor product of two cochain complexes: the de Rham complex and the complex arising from the gauge L 8-algebra L. Since the cohomology H 1 pLqof L is evidently free, Kunneth’s theorem, see e.g. [83], yields the isomorphisms H ^ 1 p pM;Lqq : à kPZ Hk ^ 1 p pM;Lqq; Hk ^ 1 p pM;Lqq à i jk 0⁄i⁄d n ”
• Hodge Laplacians on graphs (2015, methodology): “Our approach in section 2 of casting cohomology as the linear algebra of AB = 0 is the spirit of homological algebra [61].”
• A Guide for Computing Stable Homotopy Groups (2018, neutral): “One could then move on to Part III of Adams [ Ada95 ], Chapter 10.9 of Weibel [ Wei94 ] and Chapter 12 of Aguilar–Gitler–Carlos [ AGP02 ].”
• Homology of FI-modules (2015, background): “Z –Mod is a left-balanced functor in the sense of [15, Definition 2.7.7], so by [15, Exercise 2.7.4] its left-derived functors in the first variable and in the second variable coincide.”