In analogy, an action of a groupoid is a functor from the groupoid to the category of sets or to some other category.
22.
The interpretation of this theorem as a calculational tool for " fundamental groups " needs some development of ` combinatorial groupoid theory',.
23.
The smallest crystallographic hyperplane arrangement, Weyl groupoid, generalized root system, which is not of ordinary Lie type, is as follows.
24.
:A groupoid is an analog of a group in category theory : it is a small category where every morphism has an inverse.
25.
Thus when groupoids arise in terms of other structures, as in the above examples, it can be helpful to maintain the full groupoid.
26.
This groupoid plays a role in the theory of groupoids analogous to that of the group of integers in the theory of groups ".
27.
If " is instead a partial operation, then is called a "'partial magma "'or more often a partial groupoid.
28.
One then considers the fibred category which assigns to any space " B " the groupoid of families over " B ".
29.
A partial groupoid ( M, \ circ ) is called a "'partial semigroup "'if the following associative law holds:
30.
The corresponding moduli stack of smooth formal groups is a quotient of this space by a canonical action of the infinite-dimensional groupoid of coordinate changes.
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