fundamental groupoid is a certain topological invariant of a topological space. It can be viewed as an extension of the more widely-known fundamental...

homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in several equivalent ways. A groupoid can be seen...

and so on. From this ∞-groupoid we can find an n {\displaystyle n} -groupoid called the fundamental n {\displaystyle n} -groupoid Π n X {\displaystyle \Pi...

discussion of the fundamental groupoid of a topological space and the fundamental groupoid of a simplicial set Animations to introduce fundamental group by Nicolas...

in this category is an isomorphism, this category is a groupoid called the fundamental groupoid of X . {\displaystyle X.} Loops in this category are the...

the category of groupoids. This theorem gives the transition from topology to algebra, in determining completely the fundamental groupoid π 1 ( X , A )...

In mathematics, a Lie groupoid is a groupoid where the set Ob {\displaystyle \operatorname {Ob} } of objects and the set Mor {\displaystyle \operatorname...

Analogous to the fundamental groupoid it is possible to get rid of the choice of a base point and to define a monodromy groupoid. Here we consider (homotopy...

define the orbifold fundamental group. More sophisticated approaches use orbifold covering spaces or classifying spaces of groupoids. The simplest approach...

The pasting lemma is crucial to the construction of the fundamental group and fundamental groupoid of a topological space; it allows one to concatenate paths...

double groupoid generalises the notion of groupoid and of category to a higher dimension. A double groupoid D is a higher-dimensional groupoid involving...

a normal form for the fundamental groupoid of a graph of groups. In this approach there is considerable use of free groupoids on a directed graph. Grushko's...

acts on the fundamental groupoid π1(X) of the space. The semidirect product π1(X) ⋊ G is then relevant to finding the fundamental groupoid of the orbit...

definition is independent of the choice of T. The benefit in defining the fundamental groupoid of a graph of groups, as shown by Higgins (1976), is that it is defined...

Brown "Topology and Groupoids" pdf available Gives an account of some categorical methods in topology, use the fundamental groupoid on a set of base points...

then the set we get has only the structure of groupoid (which is called as the fundamental groupoid of X): two loops (under equivalence relation of...

category – Concept in category theory Formally smooth map Fundamental groupoid Fundamental group scheme Gorenstein ring – Local ring in commutative algebra...

fundamental groupoid of the orbit space X/G is isomorphic to the orbit groupoid of the fundamental groupoid of X, i.e. the quotient of that groupoid by...

matches the target of ⁠ g {\displaystyle g} ⁠. Groupoids arise in topology (for instance, the fundamental groupoid) and in the theory of stacks. Finally, it...

1007/BF01198133, S2CID 122228464. "Gives a general theorem on the fundamental groupoid with a set of base points of a space which is the union of open sets...

y ) {\displaystyle \operatorname {Hom} _{\Pi (X)}(x,y)} in the fundamental groupoid of X {\displaystyle X} has only one element. In complex analysis:...

the fundamental ∞-groupoid of X. S(X) is a quasi-category in which every morphism is invertible. The homotopy category of S(X) is the fundamental groupoid...

space, there is the notion of a fundamental groupoid (and higher variants): by definition, the fundamental groupoid of a space X is the category where...

to its action on the Teichmüller tower of Teichmüller groupoids Tg,n, the fundamental groupoids of moduli stacks of genus g curves with n points removed...

(small) groupoids into the category of (small) categories. On the other hand, the left adjoint to the above inclusion is the fundamental groupoid functor...

using the language of groupoids. The algebraic definition is easier to state: First, choose a spanning tree T in A. The fundamental group of A with respect...

In abstract algebra, a magma, binar, or, rarely, groupoid is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with...

πn(X), the nth homotopy group of X Πn(X), the fundamental n-groupoid of X Π(X), the fundamental groupoid of X πn(X), the nth cohomotopy set of X πn, a...

" ⊕ {\displaystyle \oplus } " for concatenation of paths in the fundamental groupoid and " ⊖ {\displaystyle \ominus } " for reversing the orientation...

a special case of a groupoid include: Whereas the notion of "free equivalence relation" does not exist, that of a free groupoid on a directed graph does...