On H-spaces and infinite loop spaces
On H-spaces and infinite loop spaces
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关于 H 空间和无限循环空间
DOI：
10.1007/bfb0081961
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发表时间：
1969
期刊：
影响因子：
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通讯作者：
J. Beck
中科院分区：
文献类型：
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作者：
J. Beck
对于拓扑范畴，我认为一般可以理解为一个范畴Xin，它：(1)对于每一对对象X， Ye有一个对象（X， Y）是拓扑空间，复合是一个连续的酉结合运算（X， Y） X (Y, z)（X, z）。(2)对于每一个空间a和对象Ye都有一个对象（a， Y） E和一个自然同胚(X,（）。傅。Y»(,(Xz。（3)对于每一个空间A，函子（A,）：）都有一个左伴子A X(拓扑空间的范畴本身就是一个拓扑范畴。当然，预防措施实际上是将其限制在一类空间或类似的空间中，其中转换（XxY， Z）适用。具体地说，我脑子里的是紧生成空间（E. Spanier, Annals of Math. 12(1959), 142-197，§2），但在谨慎和紧性假设下，一切都可以在拓扑空间的普通范畴中推进。
By a topological category I think is generally understood a category Xin which:(1) For each pair of objects X, Ye there is a hom object (X, Y) which is a topological space, and composition is a continuous unitary, associative operation (X, Y) x (Y, z)(X, Z).(2) For every space A and object Ye there is an object (A, Y) E and a natural homeomorphism (X,(. fu. Y»(A,(Xz. X))•(3) For every space A the functor (A,):) has a left adjoint A x (The category of topological spaces is itself a topological category. The precaution of course is actually taken of restricting to a category of spaces or something like them for which the conversion(XxY, Z) holds. Specifically, I have compactly generated spaces in mind (E. Spanier, Annals of Math. 12 (1959), 142-197, § 2), but with care and compactness assumptions everything can be pushed through in the ordinary category of topological spaces.