Sentence examples for category of categories from inspiring English sources

Lawvere from early on promoted the idea that a category of categories could be used as a foundational framework.

An alternative, suggested by Lawvere in the early sixties, is to develop an adequate language and background framework for a category of categories.

Thus ({text {Coalg}}(mathcal {C},Phi )) has a universal property similar to that of Definition 4.19, and can be thought of as a certain 2-limit in the category of categories.

This thesis also constitutes a landmark in this history of the field, for in it Lawvere proposed the category of categories as a foundation for category theory, set theory and, thus, the whole of mathematics, as well as using categories for the study of the logical aspects of mathematics.

This leads to a notion of abstract monad as simply the composition of an adjoint pair of 1-cells, one of which is the 1-cell abstracting the functor F that manufactures the free algebra F V) from V. Ordinary or concrete monads arise as the composition of functors as concrete 1-cells of a 2-category of categories.

This is in the context of Orr's own postulate of "categories of categories," namely "metrical form...resemblance form... [and] mechanical form" (confusing, yes).

L. 108 447, § 221(3)(C), substituted "purchase of the category or categories of eligible assets set forth in the sale agreement under" for "purchase of eligible assets under".

has the capacity to carry out the purchase of the category or categories of eligible assets set forth in the sale agreement under the program under this subsection and under the provisions of this paragraph.

The category (or categories) of splicing variants is a source of many differences in annotations from different annotation software tools.

Even with respect to political diversity the professoriate includes liberals, socialists, Marxists, moderates, pragmatists, libertarians, and (yes) conservatives, with many faculty claiming more than one of these categories, adding categories of their own, or rejecting any system of political categories.

This view of the categories as categories of words is also transmitted by Boethius to the Middle Ages where it becomes standard.