7 citations · 9 across the 7 of their papers we have counts for
7 papers
Nonstandard diffeology and generalized functions
Kazuhisa Shimakawa
We introduce a nonstandard extension of the category of diffeological spaces, and demonstrate its application to the study of generalized functions. Just as diffeological spaces ar…
The Quillen model structure on the category of diffeological spaces
Tadayuki Haraguchi, Kazuhisa Shimakawa
We construct on the category of diffeological spaces a Quillen model structure having smooth weak homotopy equivalences as the class of weak equivalences.
Generalized maps between diffeological spaces
Kazuhisa Shimakawa
By utilizing the idea of Colombeau's generalized function, we introduce a notion of asymptotic map between arbitrary diffeological spaces. The category consisting of diffeological…
On homotopy types of diffeological cell complexes
Tadayuki Haraguchi, Kazuhisa Shimakawa
We introduce the notion of smooth cell complexes and its subclass consisting of gathered cell complexes within the category of diffeological spaces (cf. Definitions 1 and 3). It is…
Configuration space of intervals with partially summable labels
Shingo Okuyama, Kazuhisa Shimakawa
A configuration space of intervals in with partially summable labels is constructed. It is a kind of an extension of the configuration space with partially summable l…
Homology and cohomology via enriched bifunctors
K. Shimakawa, K. Yoshida, T. Haraguchi
We show that the category of numerically generated pointed spaces is complete, cocomplete, and monoidally closed with respect to the smash product, and then utilize these features…