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3 votes

The category of posets

There is an example of a model category structure on a preorder of families of sets, defined as follows: $X\leq Y$ iff every element $x\in X$ is bounded $x\leq y_x$ by some element of $y_x\in Y$; fami …
5 votes
1 answer
680 views

comparing Hodge structures on cohomology of conjugate varieties

What can one say about the relation between the Hodge decompositions of $H^\*(X,C)$ and $H^{*}(X_\sigma,C)$ for a complex algebraic smooth projective variety $X$ and $\sigma$ an automorphism of the f …
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2 votes
0 answers
231 views

a partial order not dense iff a measurable exists

For $\kappa>0$ a regular cardinal, let $Ht_\kappa$ denote the following partial quasi-order: (i) elements(objects) of $Ht_\kappa$ are classes X of sets of size $\kappa$ with the property that, ($<_\ …
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  • 468
10 votes
0 answers
430 views

Discretifications of the fundamental group functor

Grothendieck calls a "discretification" of a profinite group $\widehat G$, a discrete group $G$ whose profinite completion is isomorphic to $\widehat G$. Does Grothendieck also define a notion of th …
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