On Braided Groupoids
نویسنده
چکیده
We study and give examples of braided groupoids, and a fortiori, non-degenerate solutions of the quiver-theoretical braid equation.
منابع مشابه
Braided N-categories and Σ-structures
We associate to any braided 2-groupoid with vanishing intermediate homotopy group a principal bundle (or torsor) endowed with a so-called Σ-structure, and show that this is the natural generalization to the 2-category context of the familiar quadratic invariant describing a braided groupoid. The corresponding structures for higher braided n-groupoids are also examined. This leads to the concept...
متن کاملO ct 1 99 8 Braided n - categories and Σ - structures Lawrence
We associate to any braided 2-groupoid with vanishing intermediate homotopy group a principal bundle (or torsor) endowed with a so-called Σ-structure, and show that this is the natural generalization to the 2-category context of the familiar quadratic invariant describing a braided groupoid. The corresponding structures for higher braided n-groupoids are also examined. This leads to the concept...
متن کاملWeak units and homotopy 3 - types
We show that every braided monoidal category arises as End(I) for a weak unit I in an otherwise completely strict monoidal 2-category. This implies a version of Simpson’s weak-unit conjecture in dimension 3, namely that one-object 3-groupoids that are strict in all respects, except that the object has only weak identity arrows, can model all connected, simply connected homotopy 3-types. The pro...
متن کاملWeak units and homotopy 3 - types For
We show that every braided monoidal category arises as End(I) for a weak unit I in an otherwise completely strict monoidal 2-category. This implies a version of Simpson’s weak-unit conjecture in dimension 3, namely that one-object 3-groupoids that are strict in all respects, except that the object has only weak identity arrows, can model all connected, simply connected homotopy 3-types. The pro...
متن کاملWeak Hopf Monoids in Braided Monoidal Categories
We develop the theory of weak bimonoids in braided monoidal categories and show them to be quantum categories in a certain sense. Weak Hopf monoids are shown to be quantum groupoids. Each separable Frobenius monoid R leads to a weak Hopf monoid R ⊗ R.
متن کامل