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, 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 unitized lumber is being shipped on flat cars, and NLRDA studies show that flat cars loaded with the new Type 6-B floating-load method can be unloaded for as little as $.054/mbf.

More recent studies suggest that the blue-green color results from small quantities of lead and water in the feldspar.

More recent research studies have shown that the principles of EVM are positive predictors of project success.

More recent studies have shown that even left-handed individuals typically have language functions only in the left hemisphere.

"</ ref > More recently, studies have suggested that sibling incest, particularly older brothers having sexual relations with younger siblings, is the most common form of incest, with some studies finding sibling incest occurring more frequently than other forms of incest.

More recent studies of entire eukaryotic genomes have now shown that the lengths and density ( introns / gene ) of introns varies considerably between related species.

More recently some studies have attempted to examine actual reactions of innocent persons generally, when faced with actual plea bargain decisions.

More recent studies have also debunked the British claims that so-called " Aryans " and " Dravidians " have a " racial divide ".

More precisely, topology studies properties that are preserved under continuous deformations, including stretching and bending, but not tearing or gluing.

Believing that More showed great potential, Morton nominated him for a place at Oxford University ( either in St. Mary's Hall ( Oriel ) or Canterbury College ), where More began his studies in 1492.

More recent studies have demonstrated that most of the magistrates ' legal work was in civil disputes, and that there was an elaborate system of civil law which used the criminal code to establish torts.

More recent morphological phylogenetic studies with this in mind placed turtles firmly within diapsids, slightly closer to Squamata than to Archosauria.

More recent studies have served to produce a reportedly fairer and more honest opinion of Leo X.

More extensive studies, however, covering far more areas and controlling for the effects of many more other gun laws, found that gun control laws generally have no detectable effect on total suicide rates.

More recent studies using DNA sequences suggest that Crustacea is paraphyletic, with the hexapods nested within a larger Pancrustacea clade.

More recent studies using more sophisticated methodologies have generally refuted these findings: density, land use and public transport accessibility can influence travel behaviour, although social and economic factors, particularly household income, usually exert a stronger influence.

Seven fine related studies of More family members also survive.

More recently, studies have concluded that: a mindfulness practice reduced mental and bodily restlessness before sleep and the subjective symptoms of insomnia ; and that mindfulness-based cognitive behavioural therapy reduced restlessness, sleep effort and dysfunctional sleep-related thoughts including worry.

More recent studies have reported similar numbers.

More recent morphological phylogenetic studies with this in mind placed turtles firmly within diapsids, some place turtles as a sister group to extant archosaurs or, more commonly within Lepidosauromorpha.

More detailed electron microscopic comparisons between cyanobacteria and chloroplasts ( for example studies by Hans Ris ), combined with the discovery that plastids and mitochondria contain their own DNA ( which by that stage was recognized to be the hereditary material of organisms ) led to a resurrection of the idea in the 1960s.

More generally there are other differences between the studies that need to be allowed for, but the general aim of a meta-analysis is to more powerfully estimate the true effect size as opposed to a less precise effect size derived in a single study under a given single set of assumptions and conditions.

" More recently in 2003, eight studies have found a positive correlation between fundamentalism and prejudice, using different measures of fundamentalism.