119 citations · 156 across the 13 of their papers we have counts for
14 papers
An ordered framework for partial multivalued functors
Alveen Chand, Ittay Weiss
The category Rel of sets and relations intimately ties the notions of function, partial multivalued function, and direct image under a function through the description of Rel as th…
The real numbers - a survey of constructions
Ittay Weiss
We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not…
The reals as rational Cauchy filters
Ittay Weiss
We present a detailed and elementary construction of the real numbers from the rational numbers a la Bourbaki. The real numbers are defined to be the set of all minimal Cauchy filt…
Metric characterization of connectedness for topological spaces
Ittay Weiss
Connectedness, path connectedness, and uniform connectedness are well-known concepts. In the traditional presentation of these concepts there is a substantial difference between co…
A folk Quillen model structure for operads
Ittay Weiss
We establish, by elementary means, the existence of a cofibrantly generated monoidal model structure on the category of operads. By slicing over a suitable operad the classical Rez…
Completion of continuity spaces with uniformly vanishing asymmetry
Alveen Chand, Ittay Weiss
The classical Cauchy completion of a metric space (by means of Cauchy sequences) as well as the completion of a uniform space (by means of Cauchy filters) are well-known to rely on…
A note on the metrizability of spaces
Ittay Weiss
With the blessing of hind sight we consider the problem of metrizability and show that the classical Bing-Nagata-Smirnov Theorem and a more recent result of Flagg give complementar…
Metric axioms: a structural study
Jorge Bruno, Ittay Weiss
For a fixed set , an arbitrary \textit{weight structure} can be interpreted as a distance assignment between pairs of points on . Restrictions…
Broad posets, trees, and the dendroidal category
Ittay Weiss
An extension of order theory is presented that serves as a formalism for the study of dendroidal sets analogously to way the formalism of order theory is used in the study of simpl…
Metric 1-spaces
Ittay Weiss
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropp…
From Operads to Dendroidal Sets
Ittay Weiss
Dendroidal sets offer a formalism for the study of -operads akin to the formalism of -categories by means of simplicial sets. We present here an account of the curr…
Dold-Kan correspondence for dendroidal abelian groups
Javier J. Gutiérrez, Andor Lukacs, Ittay Weiss
We prove a Dold-Kan type correspondence between the category of dendroidal abelian groups and a suitably constructed category of dendroidal complexes. Our result naturally extends…
On inner Kan complexes in the category of dendroidal sets
Ieke Moerdijk, Ittay Weiss
The category of dendroidal sets is an extension of that of simplicial sets, suitable for defining nerves of operads rather than just of categories. In this paper, we prove some bas…
Dendroidal Sets
Ieke Moerdijk, Ittay Weiss
We introduce the concept of a dendroidal set. This is a generalization of the notion of a simplicial set, specially suited to the study of operads in the context of homotopy theory…