## This is a collation of the operative parts of a proposal submitted to the NSF concerning

### BibTeX

@MISC{Related_thisis,

author = {Categories And Related and Mac Lane Introduced Categories and Natural Transformations},

title = {This is a collation of the operative parts of a proposal submitted to the NSF concerning},

year = {}

}

### OpenURL

### Abstract

cal structures suggests, then sustained interaction is essential. Bringing people together will result in significant technical progress and significantly greater conceptual understanding of these structures. Despite their complexity, if developed coherently, these structures, like categories themselves, should eventually become part of the standard mathematical culture. PROJECT DESCRIPTION EXPLORATIONS OF HIGHER CATEGORICAL STRUCTURES AND THEIR APPLICATIONS PROPOSED RESEARCH 1. Historical background and higher homotopies Eilenberg and Mac Lane introduced categories, functors, and natural transformations in their 1945 paper [47]. The language they introduced transformed modern mathematics. Their focus was not on categories and functors, but on natural transformations, which are maps between functors. Higher category theory concerns higher level notions of naturality, which can be viewed as maps between natural transformations, and maps between such maps, and so for