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 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 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 recent buildings like Frank Gehry's Stata Center ( 2004 ), Steven Holl's Simmons Hall ( 2002 ), Charles Correa's Building 46 ( 2005 ), Fumihiko Maki's Media Lab Extension ( 2009 ) stand out among the Boston area's classical architecture and serve as examples of contemporary campus " starchitecture ".

( More technically, when does the actual quantum state stop being a linear combination of states, each of which resembles different classical states, and instead begins to have a unique classical description?

More received a classical education at Oxford and was a pupil of Thomas Linacre and William Grocyn, becoming proficient in both Greek and Latin.

Believing women to be just as capable of academic accomplishment as men, More insisted upon giving his daughters the same classical education given to his son.

) More generally, fuzzy logic is one of many different proposed extensions to classical logic, known as probabilistic logics, intended to deal with issues of uncertainty in classical logic, the inapplicability of probability theory in many domains, and the paradoxes of Dempster-Shafer theory.

Gifford evokes both Christian and classical undertones, writing how “ Pansies – still ,/ More blest than me, thus shall ye live / Your little day ,-and when ye die ,/ Sweet flowers!

More impressive depictions of the Gigantomachy can be found in classical sculptural relief, such as the great altar of Pergamon, where the serpent-legged giants are locked in battle with a host of gods, or in Antiquity at the Temple of Olympian Zeus at Acragas.

More modern uses in classical music include Paul Hindemith's Kammermusik No. 1, op.

Along with his screen work, Schreiber is a well-respected classical actor ; in a 1998 review of the Shakespeare play Cymbeline, The New York Times called his performance " revelatory " and ended the article with the plea, " More Shakespeare, Mr. Schreiber.

The programme attracted unprecedented viewing figures for classical music ; Morrison writes, " More British people heard the LSO play in Music Night in one week than in sixty-five years of LSO concerts.

More precisely, are there hidden variables that could account for the statistical indeterminacy in a completely classical way?

More generally, V ( I ) for any ideal I is the common set on which all the " functions " in I vanish, which is formally similar to the classical definition.

More precisely, it is a solution to the equations of motion of the classical field theory on a Euclidean spacetime.

Thus the classical solutions to G Chern – Simons theory are the flat connections of principal G-bundles on M. Flat connections are determined entirely by holonomies around noncontractible cycles on the base M. More precisely, they are in one to one correspondence with equivalence classes of homomorphisms from the fundamental group of M to the gauge group G up to conjugation.

More rigorously, the mathematical operation involved in classical limits is a group contraction, approximating physical systems where the relevant action is much larger than Planck's constant ħ, so the " deformation parameter " ħ / S can be effectively taken to be zero.

WCLK airs some NPR talk programming not heard on WABE, such as The Takeaway and Tell Me More, due to WABE's mostly classical format where little talk programming is aired on that station aside from their HD channel.

More generally, it can be applied to any classical system in thermal equilibrium, no matter how complicated.

More recently, in the Summer Season ( July and August ) and during the Winter Holiday Season they provide a wide range of local entertainment, from Jazz to classical music.

More modern critics have pointed out that all the proposed rearrangements assume Propertius ' original poetry adhered strictly to the classical literary principles as set down by Aristotle, and so the apparent jumble is a result of manuscript corruptions.

In his literary criticism, More generally upheld the classical English authors who display, as he put it, a " deep-rooted sense of moral responsibility "— Shakespeare, Johnson, Trollope, Newman — while also accepting those lusty writers of France and America who cannot help but be a little too honest.