Category theory; homological algebra Categories, functors, natural transformations Concept
Quotient category
Summary
A quotient category is obtained from a category by declaring some parallel morphisms equal. The identification must be an equivalence relation on each set of morphisms that is compatible with composition, called a congruence. Quotient categories are how one builds homotopy categories, where homotopic maps become equal.
Further reading
About this page
| Tag | 43MP9NWS6H |
|---|---|
| URI | m2://43MP9NWS6H |
| Kind | concept |
| Writing | W0 stub |
| MSC | 18A32, 18A05 |
| Specializes | Category |
| Same as | |
| Changed | 2 November 2026 |
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