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In quantum field theory, there exist quantum categories. [16] [17] [18] and quantum double groupoids. [18]One can consider quantum double groupoids to be fundamental groupoids defined via a 2-functor, which allows one to think about the physically interesting case of quantum fundamental groupoids (QFGs) in terms of the bicategory Span(Groupoids), and then constructing 2-Hilbert spaces and 2 ...
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is a collection of "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object.
Abstraction is the thought process in which ideas are distanced from objects. Abstraction uses a strategy of simplification of detail, wherein formerly concrete details are left ambiguous, vague, or undefined; thus speaking of things in the abstract demands that the listener have an intuitive or common experience with the speaker, if the speaker expects to be understood.
Platonic extreme realism: beauty is a property that exists in an ideal form independently of any mind or thing. Aristotelian moderate realism or conceptualism: beauty is a property of things (fundamentum in re) [5] that the mind abstracts from these beautiful things. Nominalism: there are no universals, only individuals.
Abstract Objects: An Introduction to Axiomatic Metaphysics (1983) is the title of a publication by Edward Zalta that outlines abstract object theory.. AOT is a dual predication approach (also known as "dual copula strategy") to abstract objects [3] [4] influenced by the contributions of Alexius Meinong [5] [6] and his student Ernst Mally.
In mathematics, particularly category theory, a representable functor is a certain functor from an arbitrary category into the category of sets.Such functors give representations of an abstract category in terms of known structures (i.e. sets and functions) allowing one to utilize, as much as possible, knowledge about the category of sets in other settings.
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Roughly speaking, category theory is the study of the general form, that is, categories of mathematical theories, without regard to their content. As a result, mathematical proofs that rely on category-theoretic ideas often seem out-of-context, somewhat akin to a non sequitur. Authors sometimes dub these proofs "abstract nonsense" as a light ...