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An arrow (x, y) has a tail x, a head y, and a direction from x to y; y is said to be the direct successor to x and x the direct predecessor to y. The arrow (y, x) is the inverted arrow of the arrow (x, y). articulation point A vertex in a connected graph whose removal would disconnect the graph.
In category theory, an end of a functor : is a universal dinatural transformation from an object e of X to S. [1]More explicitly, this is a pair (,), where e is an object of X and : ¨ is an extranatural transformation such that for every extranatural transformation : ¨ there exists a unique morphism : of X with = for every object a of C.
Likewise, (x, −y) are the coordinates of its reflection across the first coordinate axis (the x-axis). In more generality, reflection across a line through the origin making an angle with the x-axis, is equivalent to replacing every point with coordinates (x, y) by the point with coordinates (x′,y′), where
If the last name ends in [a], then removing the [j] would give the name of the patriarch or the place, as in, Grudaj - j = Gruda (place in MM). Otherwise, removing the whole ending [aj] yields the name of founder or place of origin, as in Lekaj - aj = Lek(ë). Since the names are found most commonly in Malsi e Madhe (North) and Labëri (South ...
A cone with vertex N of a diagram D : J → C is a morphism from the constant diagram Δ(N) to D. The constant diagram is the diagram which sends every object of J to an object N of C and every morphism to the identity morphism on N. The limit of a diagram D is a universal cone to D. That is, a cone through which all other cones uniquely factor.
Diagram images (2 C, 1 P, 1 F) Pages in category "Diagrams" The following 175 pages are in this category, out of 175 total. ... This page was last edited on 10 May ...
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In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, [1] is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley ), and uses a specified set of generators for the group.