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Arshak Aivazian
Arshak Aivazian
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While reading the Hovey Model Category I learned that $I^{rlr} = I^r$ and $I^{lrl} = I^l$ for any setevery class of morphisms $I$ morphisms. What other relations are there between the operations of taking (weak) orthogonals? Are all $I^l, I^{ll}, I^{lll}, I^{llll}, ..$ distinct in general?

While reading the Hovey Model Category I learned that $I^{rlr} = I^r$ and $I^{lrl} = I^l$ for any set of $I$ morphisms. What other relations are there between the operations of taking (weak) orthogonals? Are all $I^l, I^{ll}, I^{lll}, I^{llll}, ..$ distinct in general?

While reading the Hovey Model Category I learned that $I^{rlr} = I^r$ and $I^{lrl} = I^l$ for every class of morphisms $I$. What other relations are there between the operations of taking (weak) orthogonals? Are all $I^l, I^{ll}, I^{lll}, I^{llll}, ..$ distinct in general?

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Arshak Aivazian
Arshak Aivazian
  • 7k
  • 1
  • 13
  • 44

Relations between the operations of taking weak orthogonals

While reading the Hovey Model Category I learned that $I^{rlr} = I^r$ and $I^{lrl} = I^l$ for any set of $I$ morphisms. What other relations are there between the operations of taking (weak) orthogonals? Are all $I^l, I^{ll}, I^{lll}, I^{llll}, ..$ distinct in general?