Questions tagged [galois-connection]

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A Galois connection arising from discussion concerning flat module and pure exact sequence

There is some sort of symmetry in the definition of flat module and pure short exact sequence which can be made precise as follows. Let $R$ be a ring (with unit), $\mathcal{R}$ be the class of all ...
Zhenhui Ding's user avatar
2 votes
0 answers
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Galois Covering induces new Cover $Ind_H ^G(Y)$

I have a question about the construction of the so called "induced cover" introduced in Tamas Szamuely's "Galois Groups and Fundamental Groups" (see page 84): We consider a group $G$ which contains a ...
user267839's user avatar
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Can lattice join be an element of residuated pair?

Given a classic (not Residuated) lattice, with standard definition of partial order via lattice join and meet operations, is it possible to satisfy Galois equivalence $$ (x \vee y) < z \;\...
Tegiri Nenashi's user avatar
26 votes
3 answers
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When does a Galois connection induce a topology?

Let $(X,\leq)$ and $(Y,\leq)$ by partially ordered sets. Recall that a(n antitone) Galois connection between $X$ and $Y$ is a pair of order-reversing maps $\Phi: X \rightarrow Y, \ \Psi: Y \...
Pete L. Clark's user avatar