Definition. Funny tensor product of categories [mde-0022]
Definition. Funny tensor product of categories [mde-0022]
Let \(ℂ, \mathbb {D}\) be small categories. Their funny tensor product \(\mathbb {C} \square \mathbb {D}\) has the following objects,
morphisms freely generated by the following,
subject to the following equations,
- \((C, h\mathbin {⨟} k) = (C,h)\mathbin {⨟}(C,k)\)
- \((i\mathbin {⨟} j, D) = (i,D)\mathbin {⨟}(j,D)\)
- \((\textsf {id}_{C}, D) = \textsf {id}_{(C,D)}\)
- \((C, \textsf {id}_{D}) = \textsf {id}_{(C,D)}.\)
This construction satisfies the universal property of the following pushout in \(\mathbf {Cat}\),
