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Topological rigidity as a monoidal equivalence
- Source :
- Communications in Algebra, Communications in Algebra, Taylor & Francis, 2019, 47 (9), pp.3457-3480. ⟨10.1080/00927872.2019.1566957⟩
- Publication Year :
- 2019
- Publisher :
- Informa UK Limited, 2019.
-
Abstract
- A topological commutative ring is said to be rigid when for every set $X$, the topological dual of the $X$-fold topological product of the ring is isomorphic to the free module over $X$. Examples are fields with a ring topology, discrete rings, and normed algebras. Rigidity translates into a dual equivalence between categories of free modules and of "topologically-free" modules and, with a suitable topological tensor product for the latter, one proves that it lifts to an equivalence between monoids in this category (some suitably generalized topological algebras) and coalgebras. In particular, we provide a description of its relationship with the standard duality between algebras and coalgebras, namely finite duality.<br />This version only deals with the monoidalily of the equivalence
- Subjects :
- coalgebras
[MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC]
Free module
010103 numerical & computational mathematics
Commutative ring
Commutative Algebra (math.AC)
Topology
01 natural sciences
[MATH.MATH-GN]Mathematics [math]/General Topology [math.GN]
Mathematics::Category Theory
finite duality
FOS: Mathematics
Category Theory (math.CT)
0101 mathematics
Equivalence (formal languages)
topological basis
[MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT]
Mathematics - General Topology
Mathematics
Algebra and Number Theory
Mathematics::Commutative Algebra
Topological dual space
010102 general mathematics
General Topology (math.GN)
Mathematics - Category Theory
Mathematics - Commutative Algebra
Subjects
Details
- ISSN :
- 15324125 and 00927872
- Volume :
- 47
- Database :
- OpenAIRE
- Journal :
- Communications in Algebra
- Accession number :
- edsair.doi.dedup.....9206757907434eedb64b542f30bd0a20