nLab local reflexive coequalizer

A bicategory has local reflexive coequalizers if each of its hom-categories has reflexive coequalizers and composition preserves them.

Similarly, a double category has local reflexive coequalizers if its loose bicategory has them.

This condition is crucial for the virtual equipment of monoids and modules in a fibrant double category $\mathbb{D}$ to be representable, i.e. to have an associative tensor of bimodules (Proposition 11.10, Shulman 2008).

References

• Mike Shulman, Framed bicategories and monoidal fibrations, Theory and Applications of Categories 20 18 (2008) 650–738 [tac:2018, arXiv:0706.1286]