-
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)...
-
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...
- ****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...
- 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...
- In mathematics, a
binary operation or
dyadic operation is a rule for
combining two
elements (called operands) to
produce another element. More formally...
-
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...
- ISBN 978-0-521-59642-8, MR 1483118 Fresse,
Benoit (2017),
Homotopy of
Operads and Grothendieck-Teichmüller Groups: Part 2: The
Applications of (Rational)...
-
several variables.
Multicategories are also
sometimes called operads, or
colored operads. A (non-symmetric)
multicategory consists of a
collection (often...
- {\mathsf {
Operads}}\subset {\tfrac {1}{2}}{\mathsf {PROP}}\subset {\mathsf {PROP}}}
where the
first category is the
category of (symmetric)
operads. An important...
