Simplicial presheaves of coalgebras
Simplicial presheaves of coalgebras
复制标题
余代数的单纯预滑
DOI：
10.2140/agt.2013.13.1967
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发表时间：
2011
影响因子：
0.7
通讯作者：
G. Raptis
中科院分区：
文献类型：
--
作者：
G. Raptis
在一个小的格罗滕迪克位点上，关于交换含幺环的预层的单纯\(R\)-余代数范畴被赋予了一个左正合的、单纯的、余可生成的模型范畴结构，其中弱等价是底层单纯预层的局部弱等价。这个模型范畴通过奎伦伴随自然地与单纯预层的\(R\)-局部同伦理论以及单纯\(R\)-模的同伦理论相关联。我们在\(R\)是代数闭（或完备）域的预层的特殊情况下研究与单纯预层的\(R\)-局部同伦范畴的比较。如果\(R\)是代数闭域的预层，我们表明单纯预层的\(R\)-局部同伦范畴完全忠实嵌入到单纯\(R\)-余代数的同伦范畴中。
The category of simplicial R-coalgebras over a presheaf of commutative unital rings on a small Grothendieck site is endowed with a left proper, simplicial, cofibrantly generated model category structure where the weak equivalences are the local weak equivalences of the underlying simplicial presheaves. This model category is naturally linked to the R-local homotopy theory of simplicial presheaves and the homotopy theory of simplicial R-modules by Quillen adjunctions. We study the comparison with the R-local homotopy category of simplicial presheaves in the special case where R is a presheaf of algebraically closed (or perfect) fields. If R is a presheaf of algebraically closed fields, we show that the R-local homotopy category of simplicial presheaves embeds fully faithfully in the homotopy category of simplicial R-coalgebras.