単一射圏実例

summary.icon

definition.icon

$ \operatorname{Obj}_\mathbf{2} = \mathbb B = \left\{ \bot, \top \right\}

射

$ \operatorname{hom}_\mathbf{2}(\bot,\bot) = \left\{ \mathrm{id}_\bot \right\}

$ \operatorname{hom}_\mathbf{2}(\bot,\top) = \left\{ \vdash \right\}

$ \operatorname{hom}_\mathbf{2}(\top,\bot) = \left\{ \right\}

$ \operatorname{hom}_\mathbf{2}(\top,\top) = \left\{ \mathrm{id}_\top \right\}

射の合成

自明なもののみ

list.icon

$ ∧\colon \mathbf{2} × \mathbf{2} → \mathbf{2}

table:product

∧ ⊥ ⊤

⊥ ⊥ ⊥

⊤ ⊥ ⊤

$ ⊃\colon \mathbf{2} × \mathbf{2} → \mathbf{2}

table:implication

⊃ ⊥ ⊤

⊥ ⊤ ⊤

⊤ ⊥ ⊤

$ \vee\colon \mathbf{2} × \mathbf{2} → \mathbf{2}

table:coproduct

∧ ⊥ ⊤

⊥ ⊥ ⊤

⊤ ⊤ ⊤

out-of.icon

$ \left\lang\mathrm{ Heyting\ algebra }\colon \mathbf{2}; ∧, ∨, ⊥, ⊤, ⊃ \right\rang

名前がないと不便なので