Omega-categories and chain complexes

There are several ways to construct omega-categories from combinatorial objects such as pasting schemes or parity complexes. We make these constructions into a functor on a category of chain complexes with additional structure, which we call augmented directed complexes. This functor from augmented directed complexes to omega-categories has a left adjoint, and the adjunction restricts to an equivalence on a category of augmented directed complexes with good bases. The omega-categories equivalent to augmented directed complexes with good bases include the omega-categories associated to globes, simplexes and cubes; thus the morphisms between these omega-categories are determined by morphisms between chain complexes. It follows that the entire theory of omega-categories can be expressed in terms of chain complexes; in particular we describe the biclosed monoidal structure on omega-categories and calculate some internal homomorphism objects.Comment: 18 pages; as published, with minor changes from version

Complicial structures in the nerves of omega-categories

It is known that strict omega-categories are equivalent through the nerve functor to complicial sets and to sets with complicial identities. It follows that complicial sets are equivalent to sets with complicial identities. We discuss these equivalences. In particular we give a conceptual proof that the nerves of omega-categories are complicial sets, and a direct proof that complicial sets are sets with complicial identities

The LaTeX project: A case study of open-source software

This is a case study of TeX, a typesetting software that was developed by Donald E. Knuth in the late 70's. Released with an open source license, it has become a reference in scientific publishing. TeX is now used to typeset and publish much of the world's scientific literature in physics and mathematics. This case study is part of a wider effort by academics to understand the open-source phenomenon. That development model is similar to the organization of the production of knowledge in academia; there is no set organization with a hierarchy, but free collaboration that is coordinated spontaneously and winds up generating complex products that are the property of all who can understand its functioning. The case study was led by gathering qualitative data via interviews with TeX developers and quantitative data on the TeX community -- the program's code, the software that is part of the TeX distribution, the newsgroups dedicated to the software, and many other indicators of the evolution and activity in that open-source project. The case study is aimed at economists who want to develop models to understand and analyze the open-source phenomenon. It is also geared towards policy-makers who would like to encourage or regulate open- source, and towards open-source developers who wonder what are the efficient strategies to make an open-source project successful.TeX, LaTeX, case study, open source, software, innovation, organisational structure, economic history, knowledge production, knowledge diffusion.

Spartan Daily, January 17, 1961

Volume 48, Issue 63https://scholarworks.sjsu.edu/spartandaily/4117/thumbnail.jp

Explaining Gabriel-Zisman localization to the computer

This explains a computer formulation of Gabriel-Zisman localization of categories in the proof assistant Coq. It includes both the general localization construction with the proof of GZ's Lemma 1.2, as well as the construction using calculus of fractions. The proof files are bundled with the other preprint "Files for GZ localization" posted simultaneously

Spartan Daily, January 17, 1961

Volume 48, Issue 63https://scholarworks.sjsu.edu/spartandaily/4117/thumbnail.jp

Psychological elements explaining the consumer's adoption and use of a website recommendation system: A theoretical framework proposal

The purpose of this paper is to understand, with an emphasis on the psychological perspective of the research problem, the consumer's adoption and use of a certain web site recommendation system as well as the main psychological outcomes involved. The approach takes the form of theoretical modelling. Findings: A conceptual model is proposed and discussed. A total of 20 research propositions are theoretically analyzed and justified. Research limitations/implications: The theoretical discussion developed here is not empirically validated. This represents an opportunity for future research. Practical implications: The ideas extracted from the discussion of the conceptual model should be a help for recommendation systems designers and web site managers, so that they may be more aware, when working with such systems, of the psychological process consumers undergo when interacting with them. In this regard, numerous practical reflections and suggestions are presented