集合论的同伦理论
Exercices de style: a homotopy theory for set theory, I
摘要：
我们从两个任意但自然的约定出发，为集合论构建了一个模型范畴（在奎伦的意义上）。它是最简单的范畴，满足我们的约定，并模拟有限性，可数性和无限等势的概念。在随后的文件\cite{GaHa1}我们给出了同伦理论字典集理论的概念，最显着的谢拉的覆盖数$\cov(λ, \aleph_1,\aleph_1,2)$，恢复从这个模型类别。我们认为，从同伦理论的角度来看，我们的建设基本上是自动遵循现有的基本方法，所以是（几乎所有）的建设工程的验证。
英文摘要：
We construct a model category (in the sense of Quillen) for set theory, starting from two arbitrary, but natural, conventions. It is the simplest category satisfying our conventions and modelling the notions of finiteness, countability and infinite equi-cardinality. In a subsequent paper \cite{GaHa1} we give a homotopy theoretic dictionary of set theoretic concepts, most notably Shelah's covering number $\cov(λ, \aleph_1,\aleph_1,2)$, recovered from this model category. We argue that from the homotopy theoretic point of view our construction is essentially automatic following basic existing methods, and so is (almost all) the verification that the construction works.
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