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, 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, the " pay-off set " ( i. e., the set of all plays in which the angel wins ) is a closed set ( in the natural topology on the set of all plays ), and it is known that such games are determined.

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.

More often than not, as the Old Grad wanders along the old paths, his memory of happy days when he strolled one of the paths with a coed beside him becomes an ache and a pain.

More recent researchers, in particular Ronald Willis and Joy Munns have studied the tour in detail and concluded that the presentation was made after a private cricket match played over Christmas 1882 when the English team were guests of Sir William Clarke, at his property " Rupertswood ", in Sunbury, Victoria.

* 1945 – More than 7, 000 die when the German refugee ship Goya is sunk by a Soviet submarine torpedo.

More generally, an n-piece cubic Bézier curve can approximate a circle, when each inner control point is the distance from an outer control point on a unit circle, where t is 360 / n degrees, and n > 2.

More recently, Peter Singer has argued that it is unreasonable that we do not give equal consideration to the interests of animals as to those of human beings when we choose the way we are to treat them.

More than one time constant is needed when describing reactions of higher order.

More broadly speaking, Chinese classic texts may refer to texts, be they written in vernacular Chinese or in classical Chinese, that existed before 1912, when the last imperial Chinese dynasty, the Qing Dynasty, fell.

More particularly, in classical mechanics, the centrifugal force is an outward force which arises when describing the motion of objects in a rotating reference frame.

More generally, to insist that all evidence converge precisely with no deviations would be naïve falsificationism, equivalent to considering a single contrary result to falsify a theory when another explanation, such as equipment malfunction or misinterpretation of results, is much more likely.

More links are then connected to that person ’ s link so you can remember what colour their shirt was, what the weather was like when you met them, etc.

More than the name separates each church example :" Independent Christian Church " will not accept a woman as a minister when some of the " Disciples of Christ " congregation will.

More precisely, a full moon occurs when the geocentric apparent ( ecliptic ) longitudes of the Sun and Moon differ by 180 degrees ; the Moon is then in opposition with the Sun .< ref >

More recently, however, different classes of spontaneous magnetization have been identified when there is more than one magnetic ion per primitive cell of the material, leading to a stricter definition of " ferromagnetism " that is often used to distinguish it from ferrimagnetism.

More generally, processes close to a massive body run more slowly when compared with processes taking place farther away ; this effect is known as gravitational time dilation.

More recently the term " cigarette boat " has replaced the term " rum-runner " when similar boats were used to smuggle cigarettes between Canada and the United States.

More generally any quadratically closed subfield of or will suffice for this purpose, e. g., the algebraic numbers, but when it is a proper subfield ( i. e., neither nor ) even finite-dimensional inner product spaces will fail to be metrically complete.

More complex multivariate analyses are sometimes used when multiple characteristics are involved and a univariate analysis could produce confounded results.

More detailed information was retrieved years later when Stasi archives were investigated by the reunited Germany.

More recently, western linguists have also tended to prefer the Latin script or the International Phonetic Alphabet ( itself largely based on Latin script ) when transcribing or creating written standards for non-European languages, such as the African reference alphabet.

More than other printmaking techniques, printmakers in lithography still largely depend on access to a good printer, and the development of the medium has been greatly influenced by when and where these have been established.

His career revival began when the young Italian director Sergio Leone boldly cast Van Cleef, whose career was still in the doldrums, as one of the two protagonists, alongside Clint Eastwood, in Leone's second western, For a Few Dollars More.

More specifically, a motion picture manuscript is called a screenplay ; a television manuscript, a teleplay ; a manuscript for the theatre, a stage play ; and a manuscript for audio-only performance is often called a radio play, even when the recorded performance is disseminated via non-radio means.

* 1960 – More than 20 million viewers watch the first televised royal wedding when Princess Margaret marries Anthony Armstrong-Jones at Westminster Abbey.

It was continued in May 1940 when Germany launched AB-Aktion, More than 16, 000 members of the intelligentsia were murdered in Operation Tannenberg alone.

More precisely, it is the instant when the Moon and the Sun have the same ecliptical longitude.