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Algebras and Hopf algebras in braided categories. (English) Zbl 0812.18004
Bergen, Jeffrey (ed.) et al., Advances in Hopf algebras. Conference, August 10-14, 1992, Chicago, IL, USA. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 158, 55-105 (1994).
This is largely a review for algebraists of algebras and Hopf algebras in braided tensor categories including the theory of braided Tannaka-Krein- type reconstruction which starts with a tensor (= strong monoidal) functor $$F:{\mathcal C} \to {\mathcal V}$$ where $${\mathcal V}$$ is braided. String diagrammatic proofs are provided. Some recent developments such as a notion of braided Lie algebra, and braided differential calculus, are discussed.
For the entire collection see [Zbl 0802.00021].

##### MSC:
 18D10 Monoidal, symmetric monoidal and braided categories (MSC2010) 18D35 Structured objects in a category (MSC2010) 16W30 Hopf algebras (associative rings and algebras) (MSC2000) 57M25 Knots and links in the $$3$$-sphere (MSC2010) 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 17B37 Quantum groups (quantized enveloping algebras) and related deformations