# Stuck with Category Theory notation. What is the meaning of 'Corner brackets' ｢ ｣?

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.

• They are defined right there in your image. – user3482749 Jan 22 at 12:41
• Do they have any special meaning? Or I can just replace them with 'g' and 'f'? – Rijndael Jan 22 at 12:53
• 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… – Luke Jan 22 at 14:32
• @Luke There's only information, that C , D and E are categories. C × DE – 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 $$\lceil D\rceil(C) = \lfloor C \rfloor(D)\ .$$