bio  website  bangor.ac.uk/r.brown 

location  
age  80  
visits  member for  4 years, 10 months 
seen  2 hours ago  
stats  profile views  4,243 
As a result of giving courses at BSc and MSc level at Liverpool, I got involved in writing a text published as "Elements of Modern Topology" with McGraw Hill in 1968, and the 3rd edition is now available as "Topology and Groupoids" from amazon, see my web page. It was writing this book, and trying to clarify certain points, such as the fundamental group of the circle, that got mew into the area of groupoids; this suggested the area of higher groupoids; research on this got going in the 1970s, and has been a major area in my work, with fortunate collaborations with Chris Spencer (197173), Philip Higgins (19742005), and JeanLouis Loday (19811985), and excellent contributions from research students.
Since 2001 I was engaged in writing a Tract giving an exposition in one place of my work since 1974 with Philip Higgins and a number of others on (strict) higher homotopy groupoids and their applications. A first step was to make available my out of print book on Topology, and this was made available in 2006 under the title "Topology and Groupoids" see my web page. The higher dimensional work was published in August, 2011, as a European Mathematical Society Tract, Vol 15, under the title "Nonabelian algebraic topology: filtered spaces, crossed complexes, cubical homotopy groupoids" with coauthors P.J. Higgins and R. Sivera.
7h

revised 
Has any attempt been made to classify finite groupoids?
typo 
10h

awarded  Necromancer 
2d

revised 
Has any attempt been made to classify finite groupoids?
added extra comments 
Mar 25 
revised 
What's special about the Simplex category?
added some extra references 
Mar 24 
revised 
What's special about the Simplex category?
more info on motives and cubical sets 
Mar 16 
comment 
Brandt's definition of groupoids (1926)
One of the fascinations of mathematics is how structures can be appropriate to help us understand the small and the large. A good example is monoidal categories which crop up for describing the family of braid groups and also of chain complexes. Charles Ehresmann wrote that his aim was to understand the structure of everything; that also includes the structure of structures! 
Mar 14 
comment 
Brandt's definition of groupoids (1926)
Martin writes "groupoids look very much like groups except that the product is only defined partially.". My definition of "higher dimensional algebra" is "the study of algebraic structures with partially defined operations whose domains are determined by geometric conditions", so that we can combine algebra and geometry, opening new worlds. Philip Higgins wrote the first paper on partial algebraic structures, "Algebras with a scheme of operators", Math. Nachr. 27 (1963) 115132. 
Mar 14 
comment 
Brandt's definition of groupoids (1926)
It is not unusual for people to be influenced by a work and then forget about that as they write and rewrite. I have probably done this. 
Mar 14 
comment 
Brandt's definition of groupoids (1926)
I have no explanation. The paper listed under General Papers no 8 at people.math.ethz.ch/~knus/publications09.html states that it is believed that the groupoid axioms influenced the work of Eilenberg and Mac Lane. 
Mar 14 
revised 
Brandt's definition of groupoids (1926)
added a reference to a translation of the Reidemeister book 
Mar 13 
answered  Brandt's definition of groupoids (1926) 
Mar 12 
comment 
Dimension leaking in homology as opposed to homotopy
@AlexDegty: The groupoid version of the SvKT using a set of base points which I published in 1967 gets over the pathconnected assumption  see the presentation referred to in my answer, and mathoverflow.net/questions/40945/… 
Mar 12 
revised 
Dimension leaking in homology as opposed to homotopy
slight clarification 
Mar 12 
answered  Dimension leaking in homology as opposed to homotopy 
Mar 11 
revised 
Compelling evidence that two basepoints are better than one
grammatical improvement to last sentence 
Mar 11 
awarded  Necromancer 
Mar 11 
revised 
Compelling evidence that two basepoints are better than one
added another link 
Mar 7 
answered  Topological Grothendieck Construction 
Mar 1 
awarded  Necromancer 
Feb 25 
revised 
Do we still need model categories?
added a link to a recent talk 