منابع مشابه
Galois symmetries of fundamental groupoids
We give a simple proof of the formula for the coproduct ∆ in the Hopf algebra of motivic iterated integrals on the affine line. We show that it encodes the group law in the group of automorphisms of certain non commutative variety. We relate the coproduct ∆ with the coproduct in the Hopf algebra of decorated rooted planar trivalent trees defined in chapter 4 – a version of the one defined by Co...
متن کاملGalois symmetries of fundamental groupoids and noncommutative geometry
We define a Hopf algebra of motivic iterated integrals on the line and prove an explicit formula for the coproduct ∆ in this Hopf algebra. We show that this formula encodes the group law of the automorphism group of a certain noncommutative variety. We relate the coproduct ∆ with the coproduct in the Hopf algebra of decorated rooted plane trivalent trees, which is a plane decorated version of t...
متن کاملA History of Selected Topics in Categorical Algebra I: From Galois Theory to Abstract Commutators and Internal Groupoids
This paper is a chronological survey, with no proofs, of a direction in categorical algebra, which is based on categorical Galois theory and involves generalized central extensions, commutators, and internal groupoids in Barr exact Mal’tsev and more general categories. Galois theory proposes a notion of central extension, and motivates the study of internal groupoids, which is then used as an a...
متن کاملn-groupoids and stacky groupoids
We discuss two generalizations of Lie groupoids. One consists of Lie n-groupoids defined as simplicial manifolds with trivial πk≥n+1. The other consists of stacky Lie groupoids G ⇒ M with G a differentiable stack. We build a 1–1 correspondence between Lie 2-groupoids and stacky Lie groupoids up to a certain Morita equivalence. We prove this in a general set-up so that the statement is valid in ...
متن کاملSlim Groupoids
Slim groupoids are groupoids satisfying x(yz) ≈ xz. We find all simple slim groupoids and all minimal varieties of slim groupoids. Every slim groupoid can be embedded into a subdirectly irreducible slim groupoid. The variety of slim groupoids has the finite embeddability property, so that the word problem is solvable. We introduce the notion of a strongly nonfinitely based slim groupoid (such g...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1971
ISSN: 0021-8693
DOI: 10.1016/0021-8693(71)90128-1