7 citations · 11 across the 11 of their papers we have counts for
15 papers
Cops and Robbers: A -homotopy Invariant Variant
Tien Chih, Laura Scull
Cops and Robbers is a pursuit-evasion game played on graphs, of which many variants have been developed and studied. We introduce a variant of this game, "Sneaky-Active Cops and Ro…
Twisted Bredon-Illman Cohomology is a Morita Invariant
Carla Farsi, Laura Scull, Jordan Watts
We show that the twisted Bredon-Illman cohomology defined by Mukherjee-Mukherjee applied to compact Lie group action groupoids is Morita-invariant. This cohomology uses coefficient…
Bicategories of Action Groupoids
Carla Farsi, Laura Scull, Jordan Watts
We prove that the 2-category of action Lie groupoids localised in the following three different ways yield equivalent bicategories: localising at equivariant weak equivalences à la…
General 2-Dimensional Adjunctions, Universal Monads and Simplicial Structures
John Lauchlin MacDonald, Laura Scull
We use the general notion of 2-dimensional adjunction with given coherence equations as introduced by MacDonald-Stone, building on earlier work by Gray, to derive coherence equatio…
Homotopy Covers of Graphs
Tien Chih, Laura Scull
We develop a theory of -homotopy, fundamental groupoids and covering spaces that apply to non-simple graphs, generalizing existing results for simple graphs. We prove that…
Fundamental Groupoids for Graphs
Tien Chih, Laura Scull
In this paper, we develop a -homotopy fundamental groupoid for graphs, and show a functorial relationship to the 2-category of graphs. We further explore the fundamental gr…
The Equivariant Fundamental Groupoid as an Orbifold Invariant
Dorette Pronk, Laura Scull
We construct a 2-category version of tom Dieck's equivariant fundamental groupoid for representable orbifolds and show that the discrete fundamental groupoid is Morita invariant; h…
Bicategories of fractions revisited: towards small homs and canonical 2-cells
Dorette Pronk, Laura Scull
This paper adresses two issues in dealing with bicategories of fractions. The first is to introduce a set of conditions on a class of arrows in a bicategory which is weaker than th…
A Homotopy Category for Graphs
Tien Chih, Laura Scull
We show that the category of graphs has the structure of a 2-category with homotopy as the 2-cells. We then develop an explicit description of homotopies for finite graphs, in term…
Classifying spaces and Bredon (co)homology for transitive groupoids
Carla Farsi, Laura Scull, Jordan Watts
We define the orbit category for transitive topological groupoids and their equivariant CW-complexes. By using these constructions we define equivariant Bredon homology and cohomol…
Endomorphisms of Exotic Models
Eugenia Ellis, Constanze Roitzheim, Laura Scull +1
We calculate the endomorphism dga of Franke's exotic algebraic model for the -local stable homotopy category at odd primes. We unravel its original abstract structure to give ex…
Atlases for Ineffective Orbifolds
Dorette Pronk, Laura Scull, Matteo Tommasini
We give a definition of atlases for ineffective orbifolds, and prove that this definition leads to the same notion of orbifold as that defined via topological groupoids.
Orbispaces and their Mapping Spaces via Groupoids: A Categorical Approach
Vesta Coufal, Dorette Pronk, Carmen Rovi +2
In this paper, we give an accessible introduction to the theory of orbispaces via groupoids. We define a certain class of topological groupoids, which we call orbigroupoids. Each o…
Spectral sequences of operad algebras
K. Bauer, L. Scull
We identify conditions under which it is guaranteed that an action of an operad on the page of a spectral sequence passes to for and hence to the pa…
Translation Groupoids and Orbifold Bredon Cohomology
Dorette Pronk, Laura Scull
We show that the bicategory of (representable) orbifolds and good maps is equivalent to the bicategory of orbifold translation groupoids and generalized equivariant maps. We use th…