拓扑刚性作为么半群等价
Topological rigidity as a monoidal equivalence
摘要：
一个拓扑交换环被称为刚性的，当对每个集合$X$，环的$X$ -fold拓扑积的拓扑对偶同构于$X$上的自由模。例子是具有环拓扑的域、离散环和赋范代数。刚性转化为自由模范畴和“拓扑自由”模范畴之间的对偶等价，并且，对于后者，利用适当的拓扑张量积，人们证明它提升为这个范畴中的幺半群（某些适当广义的拓扑代数）和余代数之间的等价。特别是，我们提供了一个描述它与代数和余代数之间的标准对偶，即有限对偶的关系。
英文摘要：
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.
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