nLab filter quotient

Idea

Given a category $\mathcal{C}$ with finite products and a suitable set of subterminal objects $\Phi$, one may construct a new category $\mathcal{C}_{\Phi}$, known as the filter quotient category, which has the same objects as $\mathcal{C}$, but where morphisms are given by equivalence classes of morphisms in $\mathcal{C}$, via an equivalence relation generated by $\Phi$.

References

• Nima Rasekh, Filter Quotient Model Structures [arXiv:2508.07735]