Department of Mathematics
The concept of big homotopy theory was introduced by J. Cannon and G. Conner in . In this paper, we seek to refine this theory by making a similar functor for specific cardinals instead of the class of all of them at the same time. It will be shown that for every topological space, there is a cardinal such that this new fundamental group agrees with the big fundamental group on that space. Between any two such functors, there is a natural transformation, including the big fundamental group and the fundamental group as classically defined in homotopy theory.
Penrod, Keith, "Big Fundamental Groups: Generalizing Homotopy and Big Homotopy" (2016). Morehouse Faculty Publications. 20.
arXiv:1410.3088v1 [math.AT] org (February 2016)