X1.3.9

  • Like the slice categories, we now consider a category derived from an existing category and two of its objects. Let \mathcal{C}_{A,B} be defined by essentially the same procedure.
  • Objects are pairs of morphisms in \mathcal{C} to A and B, and morphisms (between, say, (f_1,g_1) and (f_2,g_2) are diagrams like the following that commute: \begin{tikzcd} & & A \\ Z_1 \arrow[r, "\sigma"] \arrow[rru, "f_1", bend left] \arrow[rrd, "g_1"&39;, bend right] & Z_2 \arrow[ru, "f_2"] \arrow[rd, "g_2"] & \\ & & B\end{tikzcd}
  • Flipping the arrows gives an analogous category related to the coslice category.