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Another example of a pullback comes from the theory of fiber bundles: given a bundle map π : E → B and a continuous map f : X → B, the pullback (formed in the category of topological spaces with continuous maps) X × B E is a fiber bundle over X called the pullback bundle. The associated commutative diagram is a morphism of fiber bundles.
When =, then the pullback and the pushforward describe the transformation properties of a tensor on the manifold . In traditional terms, the pullback describes the transformation properties of the covariant indices of a tensor; by contrast, the transformation of the contravariant indices is given by a pushforward.
The pullback bundle is an example that bridges the notion of a pullback as precomposition, and the notion of a pullback as a Cartesian square. In that example, the base space of a fiber bundle is pulled back, in the sense of precomposition, above. The fibers then travel along with the points in the base space at which they are anchored: the ...
A sentence diagram is a pictorial representation of the grammatical structure of a sentence. The term "sentence diagram" is used more when teaching written language, where sentences are diagrammed .
The first published English grammar was a Pamphlet for Grammar of 1586, written by William Bullokar with the stated goal of demonstrating that English was just as rule-based as Latin. Bullokar's grammar was faithfully modeled on William Lily's Latin grammar, Rudimenta Grammatices (1534), used in English schools at that time, having been ...
The grammar model discussed in Noam Chomsky's Syntactic Structures (1957) Chomsky's transformational grammar has three parts: phrase structure rules, transformational rules and morphophonemic rules. [68] The phrase structure rules are used for expanding lexical categories and for substitutions. These yield a string of morphemes. A ...
A grammar that uses phrase structure rules is a type of phrase structure grammar. Phrase structure rules as they are commonly employed operate according to the constituency relation, and a grammar that employs phrase structure rules is therefore a constituency grammar ; as such, it stands in contrast to dependency grammars , which are based on ...
(This means that the X-bar theory indirectly assumes that speakers have in their Universal Grammar a rule that determines the canonical linear order for them, depending on their native language.) On the other hand, under the Minimalist Program, there is no such canonical fundamentals since the lexical array does not constitute an ordered set .