A Cellular Nerve for Higher Categories

A Cellular Nerve for Higher Order Categories

Introduction The following text arose from the desire to establish a rm relationship between higher order categories and topological spaces. Our approach combines the algebraic features of Michael Batanin's !-operads 1] with the geometric features of Andr e Joyal's cellular sets 15] and tries to mimick as far as possible the classical construction of the simplicial nerve of a category. Higher o...

ACellular Nerve for Higher Categories

homotopy theory, preprint, 1997. 18. W. G. Dwyer and D. M. Kan, Simplicial localizations of categories, J. Pure Appl. Algebra

Higher Operads, Higher Categories

AN INTRODUCTION TO HIGHER CLUSTER CATEGORIES

In this survey, we give an overview over some aspects of the set of tilting objects in an $m-$cluster category, with focus on those properties which are valid for all $m geq 1$. We focus on the following three combinatorial aspects: modeling the set of tilting objects using arcs in certain polygons, the generalized assicahedra of Fomin and Reading, and colored quiver mutation.

A Higher-Order Calculus for Categories

A calculus for a fragment of category theory is presented. The types in the language denote categories and the expressions functors. The judgements of the calculus systematise categorical arguments such as: an expression is functorial in its free variables; two expressions are naturally isomorphic in their free variables. There are special binders for limits and more general ends. The rules for...