40 citations · 122 across the 20 of their papers we have counts for
21 papers
Open covers, locally sectionable maps, sets of base points, and van Kampen's theorem
Ronald Brown, George Janelidze, George Peschke
We generalize the van Kampen theorem for unions of non-connected spaces, due to R. Brown and A. R. Salleh, to the context where families of subspaces of a space B are replaced by a…
Moore hyperrectangles on a space form a strict cubical omega-category
Ronald Brown
A question of Jack Morava is answered by generalising the notion of Moore paths to that of Moore hyperrectangles, so obtaining a strict cubical omega-category. This also has the st…
`Double modules', double categories and groupoids, and a new homotopical double groupoid
Ronald Brown
We give a rather general construction of double categories and so, under further conditions, double groupoids, from a structure we call a `double module'. We also give a homotopica…
Possible connections between whiskered categories and groupoids, many object Leibniz algebras, automorphism structures and local-to-global questions
Ronald Brown
We define the notion of whiskered categories and groupoids, showing that whiskered groupoids have a commutator theory. So also do whiskered -categories, thus answering questions…
Note on commutativity in double semigroups and two-fold monoidal categories
Joachim Kock
A concrete computation -- twelve slidings with sixteen tiles -- reveals that certain commutativity phenomena occur in every double semigroup. This can be seen as a sort of Eckmann-…
Pseudo Algebras and Pseudo Double Categories
Thomas M. Fiore
As an example of the categorical apparatus of pseudo algebras over 2-theories, we show that pseudo algebras over the 2-theory of categories can be viewed as pseudo double categorie…