Abstract 2 Weber

In the second lecture the two key pieces of categorical machinery useful for us -- Batanin's higher operads and Garner's algebraic weak factorisation systems -- will be reviewed. Batanin operads package the combinatorics of higher compositions in the globular framework, and a weak higher category consists of objects, arrows and higher cells which is acted on by a *contractible* higher operad. Expressing this contractibility via Garner's theory of algebraic weak factorisation systems leads to the most efficient and conceptual description of the Batanin type of definition, and also furnishes a notion of weak morphism of higher category.

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