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…