The article introduces the concept of opposites for weak globular ω-categories, showing their preservation properties. It discusses the hom functor on ω-categories and its left adjoint, the suspension functor. The paper also explores the relationship between hom ω-categories and their opposites. Higher category theory applications are highlighted, including rewriting theory, homology theory, and topological quantum field theory. The equivalence of various definitions of ω-categories is discussed, along with a new description using monads. The construction of opposites allows for unification of concepts in category theory.
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arxiv.org
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