Description of database

Each entry contains the followings fields:

• ⭐ nom: full name
  

  For example, Commutative

• abreviation: list of short names, acronyms, notations
  

  For example, Com, Comm

• ⭐ categorie: among set, Zset, vec, Zvec, dgvec
  

  Meaning: sets, ℤ-graded sets, vector spaces, ℤ-graded vector spaces, chain complexes. For Koszul sign rules, use dgvec

• ⭐ type: either symetrique, non-symetrique or shuffle
• serie: formal power series, in SageMath syntax
  

  For example x*exp(x)

• equation: algebraic or differential equation satisfied by the generating series, in SageMath syntax
  

  For example, (1-x)*P-x

• ⭐liste_dimension: list of the first dimensions, from arity 1
  

  For example, 1,2,5,14

  The convention uses weight (-t)**k for cohomological degree k.

• formule_dimension: general formula for dimension, in SageMath syntax
  

  For example, 2**n-1

• generateurs: some information about generators
  

  given as symbols with their arity, like "*": 2 or their arity and degree like "#": 2 ; 0

• relations: some information about relations
  

  As a list of equalities or linear combinations of terms, like "(x*y)*z=x*(y*z)"

• dual_koszul: full or short name of the Koszul dual operad
  

  For example, Lie

• proprietes: list among Koszul, Non-Koszul, cyclique, anticyclique, binaire, ternaire, quadratique, cubique, libre, Hopf
  

• morphismes: list of target of morphisms from this operad
  

  For example, Dendriform, Commutative

• deformations: list of deformations of this operad
  

  For example, Associative

• references: list of articles, with author names and year of publication, with preferably arxiv or doi links, or http links otherwise
• notes: text, comments, various information