Pushouts of Categories, Derived Limits, and Colimits

Abstract

We provide a counterexample to a theorem of Ford, namely a pushout square of categories with all involved functors injective, such that there is no associated exact “Mayer–Vietoris” sequence of derived limits. Further, we construct a Mayer–Vietoris sequence for derived (co)limits under some additional hypotheses, extending the well-known case of a pushout square of group monomorphisms.

Key Words:

• Derived limit
• Derived colimit
• Mayer–Vietoris sequence
• Pushout of categories

2010 Mathematics Subject Classification:

• Primary: 18G10
• Secondary: 18G15