Sentence examples for categorical framework from inspiring English sources

Two facets of the nature of mathematical objects within a categorical framework have to be emphasized.

In a categorical framework, one always refers to a token of a type, and what the theory characterizes directly is the type, not the tokens.

The categorical framework allows us to systematically define a descent homomorphism and to prove a Green–Julg theorem, a dual version of it and a generalised version that involves the action of a proper G-space.

Thus, the key here has to do with the kind of criterion of identity at work within a categorical framework and how it resembles any criterion given for objects which are thought of as forms in general.

Moreover, when developed in a categorical framework, traditional boundaries between disciplines are shattered and reconfigured; to mention but one important example, topos theory provides a direct bridge between algebraic geometry and logic, to the point where certain results in algebraic geometry are directly translated into logic and vice versa.

Doing mathematics in a categorical framework is almost always radically different from doing it in a set-theoretical framework (the exception being working with the internal language of a Boolean topos; whenever the topos is not Boolean, then the main difference lies in the fact that the logic is intuitionistic).

Conceptual relativism is a narrowly delineated form of relativism where ontology, or what exists, rather than ethical and epistemic norms, is relativized to conceptual schemes, scientific paradigms, or categorical frameworks.

It links English narratives to numbers using a categorical language framework with mathematical mappings taking the place of conjunctions and numbers.

We propose a categorical BN framework with a score-based learning algorithm that includes the class membership information in the optimization function.

New methods are needed to provide a probabilistic rather than categorical classification framework that adds a level of confidence to a diagnostic decision.

We present a categorical Bayesian network framework based on an original learning method for analysis of gene expression data, in particular, for classification of gene expression profiles coming from different populations.