# On groupoids

On groupoids,

soon,

ACL is going to write somezing we are working. Fragen comme:

1. … is a generalization of the group concept?
2. no, is not!
3. is an alg-structure X with an binary operation in a strictly proper subset.
4. i.e. $\exists A\subsetneq X$ and a $\Phi : A\to A$ such that $\Phi$ has inverses,
5. that is $\forall a_1\in A,\exists a_2\in A$ such that $\Phi(a_1,a_2)=e$
6. a bundle $F\subset E\to B$?
7. a F-bundle over a manifold?
8. abstracts the homotopy class theory of paths and loops in a topo-space pra ensamblesse o Poincare`e grouppat
9. carry-u la Bass-Serre techniques for 1d and 2d,  simplexes and complexes
10. selon Ronald Brown heretical  against the reign of gruppats
11. selon le grouppoidificatzión et spectral-categoirificatzione de juan báez de irvine califorña

meanwhile his homework is to amalgamate strategic subgroupoids of any surface to get the fundamental $\pi_1$

REF 1  John Báez: usar control-f to locate groupoidification

REF2 Ronald Brown: Groupoids in Maths