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From Wikipedia, the free encyclopedia

In mathematics, a categorical ring is, roughly, a category equipped with addition and multiplication. In other words, a categorical ring is obtained by replacing the underlying set of a ring by a category. For example, given a ring R, let C be a category whose objects are the elements of the set R and whose morphisms are only the identity morphisms. Then C is a categorical ring. But the point is that one can also consider the situation in which an element of R comes with a "nontrivial automorphism" (cf. Lurie).

This line of generalization of a ring eventually leads to the notion of an En-ring.

YouTube Encyclopedic

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  • Introduction to Higher Mathematics - Lecture 17: Rings and Fields
  • A Ring is Commutative iff (a - b)(a + b) = a^2 - b^2 Proof
  • MathHistory22: Algebraic number theory and rings I


See also


  • Laplaza, M. Coherence for distributivity. Coherence in categories, 29-65. Lecture Notes in Mathematics 281, Springer-Verlag, 1972.
  • Lurie, J. Derived Algebraic Geometry V: Structured Spaces

External links

This page was last edited on 7 August 2022, at 12:08
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