Year: 2026
Type: preprint
Abstract: The category of all topological spaces and homotopy classes of maps is cartesian closed. In fact, the $(\infty, 1)$-category of all topological spaces and continuous maps, localised at homotopy equivalences, is cartesian closed. We model the exponential object using a topological space whose points are continuous maps equipped with putative neighbourhood filters. In general, this topological space will not even be $T_1$-separated, but the evaluation map induces a natural weak homotopy equivalence witnessing the universal property.
Source: arXiv (Cornell University)
Author: Low, Zhen Lin
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222022598