対角函手

summary.icon

definition.icon

$ \Delta = \lang \Delta_{\_} \rang\colon C \to C^J

$ \forall c \colon C,\: c.\Delta = \lang \Delta_c \rang \colon C^J

where

$ J \colon \mathrm{Cat}

$ C \colon \mathrm{CAT}

$ \Delta_c \colon J → C

$ \forall j\colon J, \: j.\Delta_c = c

etc.icon

$ \Delta = {\sharp}\ast {!^{*}} = \lang {!} \ast\_^\sharp \rang \colon C \to C^J

$ \Delta_c = {!} \ast c^\sharp \colon J \to 1 \to C

$ \Delta = {!^{*}} \colon C^1 \to C^J