## Project Description:

### BibTeX

@MISC{Structures_projectdescription:,

author = {Higher Categorical Structures and Mac Lane Introduced Categories and Natural Transformations},

title = {Project Description:},

year = {}

}

### OpenURL

### Abstract

d manifolds of a certain dimension and the maps between them are equivalence classes of cobordisms between them, which are manifolds with boundary in the next higher dimension. However, it is in many respects far more natural to deal with an ncobordism "category" constructed from points, edges, surfaces, and so on through n-manifolds that have boundaries with corners. The structure encodes cobordisms between cobordisms between cobordisms. This is an n-category with additional structure, and one needs analogously structured linear categories as targets for the appropriate "functors" that define the relevant TQFT's. One could equally well introduce the basic idea in terms of formulations of programming languages that describe processes between processes between processes. A closely analogous idea has long been used in the study of homotopies between homotopies between homotopies in algebraic topology. Analogous structures appear throughout mathematics. In contrast to the original Eilenb