\(i\)を階数、\(A:\mathord {\textnormal {\textsf {Span}}}(i)\)をスパン、\(B:\mathord {\textnormal {\textsf {SpanOver}}}(A)\)を\(A\)上のスパン、\(C:\mathord {\textnormal {\textsf {Cocone}}}(A)\)を余錐、\(D:\mathord {\textnormal {\textsf {CoconeOver}}}(B,C)\)を\(C\)上の余錐とする。余錐\(\mathord {\textnormal {\textsf {Total}}}(D):\mathord {\textnormal {\textsf {Cocone}}}(\mathord {\textnormal {\textsf {Total}}}(B))\)を次のように定義する。

• -\(\mathord {\textnormal {\textsf {Vertex}}}\equiv \sum _{x:C.\mathord {\textnormal {\textsf {Vertex}}}}D.\mathord {\textnormal {\textsf {Vertex}}}(x)\)
• -\(\mathord {\textnormal {\textsf {in}}}_{\mathord {\textnormal {\textsf {Left}}}}(x)\equiv \mathord {\textnormal {\textsf {pair}}}(C.\mathord {\textnormal {\textsf {in}}}_{\mathord {\textnormal {\textsf {Left}}}}(\mathord {\textnormal {\textsf {proj}}}_{1}(x)),D.\mathord {\textnormal {\textsf {in}}}_{\mathord {\textnormal {\textsf {Left}}}}(\mathord {\textnormal {\textsf {proj}}}_{2}(x)))\)
• -\(\mathord {\textnormal {\textsf {in}}}_{\mathord {\textnormal {\textsf {Right}}}}(x)\equiv \mathord {\textnormal {\textsf {pair}}}(C.\mathord {\textnormal {\textsf {in}}}_{\mathord {\textnormal {\textsf {Right}}}}(\mathord {\textnormal {\textsf {proj}}}_{1}(x)),D.\mathord {\textnormal {\textsf {in}}}_{\mathord {\textnormal {\textsf {Right}}}}(\mathord {\textnormal {\textsf {proj}}}_{2}(x)))\)
• -\(\mathord {\textnormal {\textsf {in}}}_{\mathord {\textnormal {\textsf {Center}}}}(x)\equiv \mathord {\textnormal {\textsf {pair}}}(C.\mathord {\textnormal {\textsf {in}}}_{\mathord {\textnormal {\textsf {Center}}}}(\mathord {\textnormal {\textsf {proj}}}_{1}(x)),D.\mathord {\textnormal {\textsf {in}}}_{\mathord {\textnormal {\textsf {Center}}}}(\mathord {\textnormal {\textsf {proj}}}_{2}(x)))\)
• -\(\mathord {\textnormal {\textsf {in}}}_{\mathord {\textnormal {\textsf {leg-l}}}}(x)\)は\(\mathord {\textnormal {\textsf {pair}}}(C.\mathord {\textnormal {\textsf {in}}}_{\mathord {\textnormal {\textsf {leg-l}}}}(\mathord {\textnormal {\textsf {proj}}}_{1}(x)),D.\mathord {\textnormal {\textsf {in}}}_{\mathord {\textnormal {\textsf {leg-l}}}}(\mathord {\textnormal {\textsf {proj}}}_{2}(x)))\)に[002B]を適用して定義する。
• -\(\mathord {\textnormal {\textsf {in}}}_{\mathord {\textnormal {\textsf {leg-r}}}}(x)\)は\(\mathord {\textnormal {\textsf {pair}}}(C.\mathord {\textnormal {\textsf {in}}}_{\mathord {\textnormal {\textsf {leg-r}}}}(\mathord {\textnormal {\textsf {proj}}}_{1}(x)),D.\mathord {\textnormal {\textsf {in}}}_{\mathord {\textnormal {\textsf {leg-r}}}}(\mathord {\textnormal {\textsf {proj}}}_{2}(x)))\)に[002B]を適用して定義する。