Displaying similar documents to “Varieties of idempotent groupoids with small clones”

Fundamental pro-groupoids and covering projections

Luis Hernández-Paricio (1998)

Fundamenta Mathematicae

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We introduce a new notion of covering projection E → X of a topological space X which reduces to the usual notion if X is locally connected. We use locally constant presheaves and covering reduced sieves to find a pro-groupoid π crs (X) and an induced category pro (π crs (X), Sets) such that for any topological space X the category of covering projections and transformations of X is equivalent to the category pro (π crs (X), Sets). We also prove that the latter category is equivalent...

Inner Products, Group, Ring of Quaternion Numbers

Fuguo Ge (2008)

Formalized Mathematics

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In this article, we define the division of the quaternion numbers, we also give the definition of inner products, group, ring of the quaternion numbers, and we prove some of their properties.MML identifier: QUATERN2, version: 7.8.10 4.100.1011