# Cohomology theory of abelian groups and homotopy theory I.

@article{Eilenberg1950CohomologyTO, title={Cohomology theory of abelian groups and homotopy theory I.}, author={Samuel Eilenberg and Saunders Maclane}, journal={Proceedings of the National Academy of Sciences of the United States of America}, year={1950}, volume={36 8}, pages={ 443-7 } }

## 58 Citations

Braided Picard groups and graded extensions of braided tensor categories

- MathematicsSelecta Mathematica
- 2021

We classify various types of graded extensions of a finite braided tensor category $\cal B$ in terms of its $2$-categorical Picard groups. In particular, we prove that braided extensions of $\cal B$…

Higher cohomologies of modules

- Mathematics
- 2012

If C is a small category, then a right C–module is a contravariant functor from C into abelian groups. The abelian category ModC of right C–modules has enough projective and injective objects, and…

Monoidal Functors, Species, and Hopf Algebras

- Mathematics
- 2010

This research monograph integrates ideas from category theory, algebra and combinatorics. It is organised in three parts. Part I belongs to the realm of category theory. It reviews some of the…

Gerbe-holonomy for surfaces with defect networks

- Mathematics
- 2008

We define the sigma-model action for world-sheets with embedded defect networks in the presence of a three-form field strength. We derive the defect gluing condition for the sigma-model fields and…

Higher braidings of diagonal type

- Mathematics
- 2022

. Heckenberger introduced the Weyl groupoid of a ﬁnite dimensional Nichols algebra of diagonal type. We replace the matrix of its braiding by a higher tensor and present a construction which yields…

Orbifolds and minimal modular extensions

- Mathematics
- 2021

Let V be a simple, rational, C2-cofinite vertex operator algebra and G a finite group acting faithfully on V as automorphisms, which is simply called a rational vertex operator algebra with a…

Finite quasi-quantum groups of rank two

- MathematicsTransactions of the American Mathematical Society, Series B
- 2021

This is a contribution to the structure theory of finite pointed quasi-quantum groups. We classify all finite-dimensional connected graded pointed Majid algebras of rank two which are not twist…

Braided categorical groups and strictifying associators

- MathematicsHomology, Homotopy and Applications
- 2020

A key invariant of a braided categorical group is its quadratic form, introduced by Joyal and Street. We show that the categorical group is braided equivalent to a simultaneously skeletal and…