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A sheaf is a presheaf with "something" added allowing us to define things locally. This task is forbidden for presheaves in general. Specifically, a presheaf F on a ...

Suppose that A and B are two algebras and M is a unital A-B-bimodule. Then [A M; 0 B]={[a m; 0 b]:a in A,m in M,b in B} with the usual 2×2 matrix-like addition and ...

An expression is called "well-defined" (or "unambiguous") if its definition assigns it a unique interpretation or value. Otherwise, the expression is said to not be ...

The hemiobelisk graph is the skeleton of the hemiobelisk. It has 7 vertices, 11 edges, and 6 faces. It is a minimal unit-distance forbidden graph. It is implemented in the ...

The hemicubical graph is the skeleton of the hemicube. It has 7 vertices, 11 edges, and 6 faces. It is implemented in the Wolfram Language as GraphData["HemicubicalGraph"].

Ball and Coxeter (1987, pp. 277-278) define the ladder graph nP_2, here called the ladder rung graph, of order n as the graph union of n copies of the path graph P_2. The ...

An idoneal number, also called a suitable number or convenient number, is a positive integer D for which the fact that a number is a monomorph (i.e., is expressible in only ...

The Lemke graph is the 8-node graph with 13 edges illustrated above (Lemke and Kleitman 1989, Hurlbert 2011, Hurlbert 2013). The Lemke graph is the smallest graph that does ...

If p and q are distinct odd primes, then the quadratic reciprocity theorem states that the congruences x^2=q (mod p) x^2=p (mod q) (1) are both solvable or both unsolvable ...

The Greenfield graph is the name given in this work to the 12-vertex graph illustrated above due to Greenfield (2011). This graph provided the first known example which ...