bio  website  bangor.ac.uk/r.brown 

location  
age  80  
visits  member for  5 years 
seen  5 hours ago  
stats  profile views  4,358 
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.
2d

comment 
What's a groupoid? What's a good example of a groupoid?
This discussion should be linked to mathoverflow.net/questions/40945/… 
May 20 
revised 
Is there a (satisfying) proof that cellular cohomology is isomorphic to simplicial cohomology that doesn't use relative cohomlogy?
added a link 
May 19 
awarded  Yearling 
May 14 
answered  Is there a (satisfying) proof that cellular cohomology is isomorphic to simplicial cohomology that doesn't use relative cohomlogy? 
May 14 
awarded  Necromancer 
May 10 
awarded  Nice Answer 
May 2 
answered  Exact sequences of pointed sets  two definitions 
Mar 30 
revised 
Has any attempt been made to classify finite groupoids?
typo and word order 
Mar 30 
comment 
Has any attempt been made to classify finite groupoids?
@Qiaochu Yuan: Groupoids equipped with a $G$action where $G$ is a group occur in the study of orbit spaces, where the groupoid is the fundamental groupoid $\pi_1(X)$. See Chapter 11 of Topology and Groupoids, where the "orbit groupoid" is related to the fundamental groupoid of the orbit space! 
Mar 29 
revised 
Has any attempt been made to classify finite groupoids?
typo 
Mar 29 
awarded  Necromancer 
Mar 27 
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) 