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D - Form of SMARANDACHE GROUPOID [PDF]
, 2000 This article is about D - Form of SMARANDACHE ...
Talukdar, D.
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Journal of Algebra, 2007 We study and give examples of braided groupoids, and, a fortiori, non-degenerate solutions of the quiver-theoretical braid equation.
Maldonado, Carolina +1 more
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Smarandache Fuzzy Algebra [PDF]
, 2003 groupoid semi group semigroup group loop group groupoid semigroup loop semi group group ...
Vasantha, Kandasamy +2 more
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Fundamental Groupoids for Graphs [PDF]
Categories and General Algebraic Structures with Applications, 2022 In recent years several notions of discrete homotopy for graphs have been introduced, including a notion of ×-homotopy due to Dochtermann. In this paper, we define a ×-homotopy fundamental groupoid for graphs, and prove that it is a functorial ×-homotopy
Tien Chih, Laura Scull
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Extendibility, monodromy, and local triviality for topological groupoids
International Journal of Mathematics and Mathematical Sciences, 2001 A groupoid is a small category in which each morphism has an inverse. A topological groupoid is a groupoid in which both sets of objects and morphisms have topologies such that all maps of groupoid structure are continuous.
Osman Mucuk, İlhan İçen
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Constructing Higher Inductive Types as Groupoid Quotients [PDF]
Logical Methods in Computer Science, 2021 In this paper, we study finitary 1-truncated higher inductive types (HITs) in homotopy type theory. We start by showing that all these types can be constructed from the groupoid quotient.
Niccolò Veltri, Niels van der Weide
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The fundamental groupoid as a topological groupoid [PDF]
Proceedings of the Edinburgh Mathematical Society, 1975 Let X be a topological space. Then we may define the fundamental groupoid πX and also the quotient groupoid (πX)/N for N any wide, totally disconnected, normal subgroupoid N of πX (1). The purpose of this note is to show that if X is locally path-connected and semi-locally 1-connected, then the topology of X determines a “lifted topology” on (πX)/N so ...
Brown, R., Danesh-Naruie, G.
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Types Are Internal ∞-Groupoids [PDF]
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2021 By extending type theory with a universe of definitionally associative and unital polynomial monads, we show how to arrive at a definition of opetopic type which is able to encode a number of fully coherent algebraic structures. In particular, our approach leads to a definition of -groupoid internal to type theory and we prove that the type of such ...
Eric Finster +2 more
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n-Groupoids and Stacky Groupoids [PDF]
International Mathematics Research Notices, 2009 We discuss two generalizations of Lie groupoids. One consists of Lie $n$-groupoids defined as simplicial manifolds with trivial $π_{k\geq n+1}$. The other consists of stacky Lie groupoids $\cG\rra M$ with $\cG$ a differentiable stack. We build a 1-1 correspondence between Lie 2-groupoids and stacky Lie groupoids up to a certain Morita equivalence.
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