While reading an article, I encountered this expression. Expression

I was wondering if anyone knows what does the corner brackets 「(upper) and 」(down) in this expression do?

Thank you.

  • 5
    $\begingroup$ They are defined right there in your image. $\endgroup$ – user3482749 Jan 22 at 12:41
  • $\begingroup$ Do they have any special meaning? Or I can just replace them with 'g' and 'f'? $\endgroup$ – Rijndael Jan 22 at 12:53
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    $\begingroup$ Some context would be helpful (in addition to correct grammar): Is there any mention of what category $\mathscr{E}$ is? Because $\lceil {C} \rceil D$ is just an object in $\mathscr{E}$ and an object in $\mathscr{D}$ written consecutively… $\endgroup$ – Luke Jan 22 at 14:32
  • $\begingroup$ @Luke There's only information, that C , D and E are categories. C × DE $\endgroup$ – Rijndael Jan 22 at 14:45

It is not a standard notation, but it is clearly stated that they are functions of the forms $$ \begin{align*} \lceil\ \rceil \colon Ob(\mathcal D) \to [\mathcal C,\mathcal E]\\ \lfloor \ \rfloor \colon Ob(\mathcal C) \to [\mathcal D, \mathcal E] \end{align*} $$ satisfying the equation $$ \lceil D\rceil(C) = \lfloor C \rfloor(D)\ . $$

From the nature of the equation I suppose that there is a bifunctor lurking around, but I cannot be sure with the limited amount of details provided.


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