-
rational homotopy theory could be
explained using Koszul duality of
operads.
Operads have
since found many applications, such as in
deformation quantization...
- (where n ∈ N). In the
setting of non-Σ
operads (also
termed nonsymmetric operads,
operads without permutation), an
operad A is A∞ if all of its
spaces A(n)...
- In the
theory of
operads in
algebra and
algebraic topology, an E∞-
operad is a
parameter space for a
multiplication map that is ****ociative and commutative...
-
operads", Duke
Mathematical Journal, 76 (1): 203–272, doi:10.1215/S0012-7094-94-07608-4, MR 1301191 Todd Trimble,
Notes on
operads and the Lie
operad...
-
distributive over colimits. If f : O → O ′ {\displaystyle f:O\to O'} is a map of
operads and, moreover, if f is a
homotopy equivalence, then the ∞-category of algebras...
-
equivalence between Lurie's
model and the
dendroidal model for infinity-
operads".
Advances in Mathematics. 302: 869–1043. arXiv:1305.3658. doi:10.1016/j...
- in 2000 with a Ph.D. from the
University of Cambridge. His Ph.D.
thesis Operads in Higher-Dimensional
Category Theory was
supervised by
Martin Hyland....
- ****ociative
operad is self-dual,
while the
commutative and the Lie
operad correspond to each
other under this duality.
Koszul duality for
operads states an...
- geometry; supersymmetry;
operads; and Hopf algebras. He
retired in 2014. A 2002 book of Markl,
Shnider and
Stasheff Operads in algebra, topology, and...
- Furthermore,
Ginzburg and
Mikhail Kapranov developed Koszul duality theory for
operads. In
noncommutative geometry,
Ginzburg defined,
following earlier ideas...
