Operadic Definition of Non-Stricts Cells

TL;DR

This paper introduces an operadic framework for non-strict higher categories, extending Batanin's approach with globular colored contractible operads to define non-strict infinity-functors and transformations.

Contribution

It provides a new operadic definition of non-strict higher cells based on Batanin's contractible operads, expanding the algebraic tools for higher category theory.

Findings

Defines non-strict infinity-functors using globular colored contractible operads.

Extends Batanin's operadic approach to non-strict higher categories.

Provides a categorical framework compatible with higher-dimensional structures.

Abstract

In [K. Kachour. D\'efinition alg\'ebrique des cellules non-strictes. Cahiers de Topologie et de G\'eom\'etrie Diff\'erentielle Cat\'egorique, 1:1-68, 2008] we pursue Penon's work in higher dimensional categories by defining non-strict infinity-functors, non-strict natural infinity-transformations, and so on, all that with Penon's frameworks i.e with the "\'etirements cat\'egoriques", where we have used an extension of this object, namely the "n-\'etirements cat\'egoriques" (n belong in N). In this paper we are pursuing Batanin's work in higher dimensional categories by defining nonstrict infinity-functors, non-strict natural infinity-transformations, and so on, using Batanin's frameworks i.e with the contractible operads, where we used an extension of this object, namely the globular colored contractible operads.