The rule permits the movement of any phrasal or lexical category from one part of a sentence to another in such a way that the operation involves substitution or ( Chomsky-) adjunction.
42.
Consequently, Beck's monadicity theorem, which gives a criterion for monadicity, can be used to show that an arbitrary adjunction can be treated as a category of algebras in this way.
43.
In the category of abelian groups, pushouts can be thought of as " direct sum with gluing " in the same way we think of adjunction spaces as " disjoint union with gluing ".
44.
"' Q "'is interpretable in a fragment of Zermelo's axiomatic set theory, consisting of extensionality, existence of the empty set, and the axiom of adjunction.
45.
This follows because there is an adjunction between simplicial sets and simplicial commutative rings ( given by the forgetful and free functors ), and in nice cases one can lift model structures under an adjunction.
46.
This follows because there is an adjunction between simplicial sets and simplicial commutative rings ( given by the forgetful and free functors ), and in nice cases one can lift model structures under an adjunction.
47.
One can verify directly that this correspondence is a natural transformation, which means it is a hom-set adjunction for the pair ( " F ", " G " ).
48.
For every adjunction ( \ varepsilon, \ delta ), the morphological opening \ gamma \ colon L \ rightarrow L and morphological closing \ phi \ colon L \ rightarrow L are defined as follows:
49.
Furthermore, the approach is meant to allow the dynamic adjunction of a path in the map, i . e . adding a new strategy or a new section in the actual course of the process.
50.
Most local councils were entirely Bulgarian or were dominated by Bulgarians and decided in favour of their co-nationals far more often than did the mixed commissions with whom the prerogative of adjunction had previously rested.
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