| 词汇 | example_english_pullback |
| 释义 | Examples of pullbackThese examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. Furthermore, since the bottom, front and top squares are pullbacks, the back square is also a pullback. This category has weak pullbacks and setindexed products, but, in general, no pullbacks. The interior operation is not assumed to be natural; that is, it is not assumed to commute with pullbacks. First it can be easily checked that the following diagram is a pullback. For example, collections can be zipped if and only if the monad's endofunctor preserves pullbacks. We will also have use for inverse images, which are pullbacks of two morphisms at least one of which is a monomorphism. The role of pullbacks in categorical interpretations of logic is to perform substitution of terms into predicates and formulas. Let be a weak inclusive category that has pullbacks. The gist of affine equivalence techniques is to use these estimates in combination with the pullback formulas (2.16)-(2.19) for vector proxies. Techniques based on the pullback of differential forms are instrumental in getting interpolation estimates. Let us note a general 2-categorical fact, that pullback functors between slices preserve existing exponentials. For the rest, we add as before the pullback tiles that provide the coordination mechanism about local instantiations. Then (1) is a pullback if and only if it satisfies the reduced chain-condition and f, g is monomorphic. Indeed, to interpret substitution, we need to find a canonical choice of pullbacks that is functorial and is strictly preserved by the categorical structure. Here we require that the category must be at least lex, since we want to interpret substitution via pullback. The category of stochastic relations is shown not to have (weak) pullbacks. It can be readily verified that the diagram is also a pullback. This time the function exists to make the whole diagram commute by the universal property of the lower quadrangle as a pullback. It provides a way to control distortion in terms of diameters of a bounded degree pullback. If the outer square is a pullback, so is (1). This section is concerned with giving preservation properties of the morphisms from both and by pushouts and pullbacks, respectively. The last section of the paper investigates pushout and pullback properties of weak inclusion systems. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
反思网英语在线翻译词典收录了377474条英语词汇在线翻译词条，基本涵盖了全部常用英语词汇的中英文双语翻译及用法，是英语学习的有利工具。