The relationship between the diagonal and the bar constructions on a bisimplicial set

AbstractThe aim of this paper is to prove that the homotopy type of any bisimplicial set X is modelled by the simplicial set W¯X, the bar construction on X. We stress the interest of this result by showing two relevant theorems which now become simple instances of it; namely, the Homotopy colimit theorem of Thomason, for diagrams of small categories, and the generalized Eilenberg–Zilber theorem of Dold–Puppe for bisimplicial Abelian groups. Among other applications, we give an algebraic model for the homotopy theory of (not necessarily path-connected) spaces whose homotopy groups vanish in degree 4 and higher

Environmental knowledge management: A long-term enabler of tourism development

A review of the literature confirms that there is a need for knowledge management frameworks which support knowledge creation, particularly in those organisations having to operate in a changing environment. Socialisation, externalisation, combination and internalisation continue to be key processes for the creation of knowledge which enables organisations to successfully address environmental challenges. This paper examines the relevance and importance of a SECI model as an enabler of the processes of reusing and updating the environmental knowledge of an organisation. The research reported has confirmed that time is a key component of the implementation of a SECI model in organisations operating in a changing environment. Thins been confirmed that such a strategy should focus on the reuse of prior environmental knowledge as a mechanism to establish within the organisation a context where new knowledge management processes are understood and adopted by employees. The paper also examines the relationship between environmental knowledge and organisational performance indicators. These relationships are examined through an empirical study of 87 companies in the Spanish hospitality sector. The results of the study indicate that environmental knowledge at any given time (T) is significant in predicting the knowledge management processes that may be successfully implemented at a later point in time (T + 6 years). (C) 2015 Elsevier Ltd. All rights reserved

From double Lie groupoids to local Lie 2-groupoids

We apply the bar construction to the nerve of a double Lie groupoid to obtain a local Lie 2-groupoid. As an application, we recover Haefliger's fundamental groupoid from the fundamental double groupoid of a Lie groupoid. In the case of a symplectic double groupoid, we study the induced closed 2-form on the associated local Lie 2-groupoid, which leads us to propose a definition of a symplectic 2-groupoid.Comment: 23 pages, a few minor changes, including a correction to Lemma 6.