11 citations · 17 across the 9 of their papers we have counts for
9 papers
-manifolds with skeletal diffeology
Hiroshi Kihara
We formulate and study the notion of -skeletal diffeology, which generalizes that of wire diffeology, introducing the dual notion of -coskeletal diffeology. We first show tha…
Smooth singular complexes and diffeological principal bundles
Hiroshi Kihara
In previous papers, we used the standard simplices endowed with diffeologies having several good properties to introduce the singular complex $S^\dcal(X)$ of a dif…
Phantom maps and rational homotopy
Hiroshi Kihara
We generalize theorems of McGibbon-Roitberg, Iriye, and Meier on the relations between phantom maps and rational homotopy, and apply them to provide new calculational examples of t…
Phantom maps and fibrations
Hiroshi Kihara
Given pointed -complexes and , $\rmph(X, Y)$ denotes the set of homotopy classes of phantom maps from to and $\rmsph(X, Y)$ denotes the subset of $\rmph(X, Y)$ c…
Smooth Homotopy of Infinite-Dimensional -Manifolds
Hiroshi Kihara
In this paper, we use homotopical algebra (or abstract homotopical methods) to study smooth homotopical problems of infinite-dimensional -manifolds in convenient calculus…
Quillen equivalences between the model categories of smooth spaces, simplicial sets, and arc-gengerated spaces
Hiroshi Kihara
In the preceding paper, we have constructed a compactly generated model structure on the category $\dcal$ of diffeological spaces together with the adjoint pairs $|\ |_\dcal : \sca…
Model category of diffeological spaces
Hiroshi Kihara
The existence of a model structure on the category of diffeological spaces is crucial to developing smooth homotopy theory. We construct a compactly generated model s…
Cogroups in the category of connected graded algebras whose inverse and antipode coincide
Hiroshi Kihara
Let A be a cogroup in the category of connected graded algebras over a commutative ring R. Let nu denote the inverse of A and chi the antipode of the underlying Hopf algebra of A.…
Minimal fibrations and the organizing theorem of simplicial homotopy theory
Hiroshi Kihara
Quillen showed that simplicial sets form a model category (with appropriate choices of three classes of morphisms), which organized the homotopy theory of simplicial sets. His proo…