3.3.4 The Right Annihilator

The right annihilator of the product of sets is the natural isomorphism

\[ \zeta ^{\mathsf{Sets}}_{r} \colon \mathbb {0}^{\mathsf{Sets}}\circ \mathbf{\mu }^{\mathsf{Cats}_{\mathsf{2}}}_{4|\mathsf{Sets},\mathsf{Sets},\mathsf{Sets},\mathsf{Sets}}\circ \webleft (\mathbf{\epsilon }^{\mathsf{Cats}_{\mathsf{2}}}_{\mathsf{Sets}}\times \text{id}_{\mathsf{pt}}\webright ) \overset {\scriptstyle \mathord {\sim }}{\dashrightarrow }\times \circ \webleft (\text{id}_{\mathsf{Sets}}\times \mathbb {0}^{\mathsf{Sets}}\webright ) \]

as in the diagram

with components

\[ \zeta ^{\mathsf{Sets}}_{r|A}\colon A\times \text{Ø}\overset {\scriptstyle \mathord {\sim }}{\dashrightarrow }\text{Ø}. \]


Noticed something off, or have any comments? Feel free to reach out!


You can also use the contact form below: