# All Questions

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### Can such categorical notion of action be formalized?

I'm wondering if it's possible to find an universal construction for a general concept of action for (single-sorted?) finite product sketches, such that one of those is "acting" on the second in the ...
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### Example of measure of non-compactness

I can't understand the following example of measure of non-compactness, which was given in this article. Definition: A non-negative function $\phi$ defined on the bounded subsets of $X$ will be ...
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### Category theory for Algebraic Geometry

How much of category theory should I know to view schemes, sheaves and cohomology concepts as concrete cases of abstract categorical concepts? Is there a textbook of category theory for AG people?
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### bar construction and loop space cohomology

Let $X$ be a topological space. Then its chain complex $C_{*}(X)$ is naturally a coalgebra (as explained here Does homology have a coproduct?). In particular if $X$ is simply connected we have that ...
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### Are Sobolev trace spaces equal from both sides of the boundary?

Let $\Omega\subset\mathbb R^n$ be a bounded open set and $\Omega'$ the complement of its closure. Assume $\partial\Omega=\partial\Omega'$. Are the quotient spaces $W^{1,p}(\Omega)/W^{1,p}_0(\Omega)$ ...