More abstractly, one talks about the product in category theory, which formalizes these notions.

More abstractly, Campbell's idea that myths are how we shape our lives deeply informs the picture of life in Glorantha throughout the game world's publication history.

More abstractly, the convex-hull operator Conv () has the characteristic properties of a closure operator:

More abstractly, one can define the dicyclic group Dic < sub > n </ sub > as any group having the presentation

More abstractly, when using infix notation

More abstractly, the symplectic group can be defined as the set of linear transformations of a 2n-dimensional vector space over F that preserve a nondegenerate, skew-symmetric, bilinear form.

More abstractly, in classical mechanics phase space is the cotangent space of configuration space, and in this interpretaton the procedure above expresses that a choice of local coordinates on configuration space induces a choice of natural local Darboux coordinates for the standard symplectic structure on a cotangent space.

More abstractly and more precisely, it may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such a square.

More abstractly, the integral can be written as the cap product of the homology class of Z and the cohomology class represented by α.

More abstractly, it can be defined as an incidence structure ( P, L, I ) consisting of a set P of points, a set L of lines, and an incidence relation I stating which points lie on which lines.

More generally and abstractly, given any group G and a representation of G on a vector space V,

More abstractly, it means that the cohomology class in the classifying space for pulls back from the cohomology class in under the inclusion ( which corresponds to the inclusion and similar ).

so too is the dual group More abstractly, these are both examples of representable functors, being represented respectively by K and T.

The order of PSL ( n, q ) is the above, divided by, the number of scalar matrices with determinant 1 – or equivalently dividing by, the number of classes of element that have no nth root, or equivalently, dividing by the number of nth roots of unity in .< ref group =" note "> These are equal because they are the kernel and cokernel of the endomorphism formally, More abstractly, the first realizes PSL as SL / SZ, while the second realizes PSL as the kernel of

More abstractly, a conservative vector field is an exact 1-form.

More generally, if W is a linear subspace of a ( possibly infinite dimensional ) vector space V then the codimension of W in V is the dimension ( possibly infinite ) of the quotient space V / W, which is more abstractly known as the cokernel of the inclusion.

More abstractly, it studies how global properties of a graph influence local substructures of the graph.

More abstractly, the mean curvature is the trace of the second fundamental form divided by n ( or equivalently, the shape operator ).

More abstractly, some aspects of the narrative appear in the crucifixion story of Jesus found in the gospels.

More abstractly: If X < sub > 1 </ sub >, ..., X < sub > n + 1 </ sub > are conditionally independent random variables that each can assume the value 0 or 1, then, if we know nothing more about them,

More abstractly and generally, we note that the two quantities asserted to be equal count the subsets of size k and n − k, respectively, of any n-element set S. There is a simple bijection between the two families F < sub > k </ sub > and F < sub > n − k </ sub > of subsets of S: it associates every k-element subset with its complement, which contains precisely the remaining n − k elements of S. Since F < sub > k </ sub > and F < sub > n − k </ sub > have the same number of elements, the corresponding binomial coefficients must be equal.

More abstractly, f is proper if for any space Z the map

More abstractly, " G-bundles over X " is a functor in G: given a map H → G, one gets a map from H-bundles to G-bundles by inducing ( as above ).

More abstractly, a natural class of objects to study in topology are objects that are homogeneous ( all points are topologically the same: the group of self-homeomorphisms acts transitively ) and " finite type " or " tame " ( to rule out spaces such as the Cantor set, where each open set contains uncountably many connected components ); more generally, a space of " finite type " where the self-homeomorphism group has finitely many orbits, forming the strata.

The actual function of patristic communism was adequately set forth by St. Gregory almost a millenium before More wrote Utopia.

More precisely, a binary operation on a non-empty set S is a map which sends elements of the Cartesian product S × S to S:

More formally a k-combination of a set S is a subset of k distinct elements of S. If the set has n elements the number of k-combinations is equal to the binomial coefficient

More recently, an effort to replace CPAN. pm with something cleaner and more modern has resulted in the CPANPLUS or CPAN ++ set of modules.

More recently, beginning at the 1997 CHOGM, the meeting has had an official ' theme ', set by the host nation, on which the primary discussions have been focused.

More soldiers were now arriving and three weeks later a force of 20, 000 set off again to relieve Peking.

More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions.

More precisely, he showed that a random graph on vertices, formed by choosing independently whether to include each edge with probability has, with probability tending to 1 as goes to infinity, at most cycles of length or less, but has no independent set of size Therefore, removing one vertex from each short cycle leaves a smaller graph with girth greater than in which each color class of a coloring must be small and which therefore requires at least colors in any coloring.

More explicitly, the action groupoid is the set with source and target maps s ( g, x )

More flexibility in selecting which strings play is available in harpsichords having more than one keyboard or manual, since each manual can control the plucking of a different set of strings.

More complex rewritings involving modus tollens are often seen, for instance in set theory:

More specifically, the term describes the modernist movement in the arts, its set of cultural tendencies and associated cultural movements, originally arising from wide-scale and far-reaching changes to Western society in the late 19th and early 20th centuries.

More recently, a comprehensive set of machine-checked proofs has been performed of the properties of the protection model of seL4, a version of L4.

More generally, whenever an ideal is taken as understood, then a null set is any element of that ideal.

More specifically, it is the set of expressed proteins in a given type of cells or an organism at a given time under defined conditions.

* The More Short Trips short story " Special Weapons ", set late in season 24, indicates that the Seventh Doctor has a sonic screwdriver.

More generally, in a metric space ( E, d ), the sphere of center x and radius is the set of points y such that.

More importantly, the Giants set an NFL record by losing only 14 turnovers in a 16-game regular season.

More generally, one can define objects by transfinite recursion on any well-founded relation R. ( R need not even be a set ; it can be a proper class, provided it is a set-like relation ; that is, for any x, the collection of all y such that y R x must be a set.

The success More enjoyed in educating his daughters set an example for other noble families.

At the request of Henry VIII, More set about composing a rebuttal: the resulting Responsio ad Lutherum was published at the end of 1523.

More specifically, HTML 4. 0 documents are required to consist of characters in the HTML document character set: a character repertoire wherein each character is assigned a unique, non-negative integer code point.

More sophisticated transformations include set operations on closed shapes ( union, difference, intersection, etc.