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We give sufficient conditions for effective descent in categories of (generalized) internal multicategories. Two approaches to study effective descent morphisms are pursued. The first one relies on establishing the category of internal multicategories as an equalizer of categories of diagrams. The second approach extends the techniques developed by Ivan Le Creurer in his study of descent for internal essentially algebraic structures.

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We study descent for (generalized) internal multicategories. Two approaches to the problem are given. The first one relies on establishing the category of internal multicategories as an equalizer of categories of diagrams. The second approach follows the techniques developed by Ivan Le Creurer in his study of descent for internal categories. Contents 4 3. First approach 4. Second approach 5. Note on examples Appendix A. Image of the Eilenberg-Moore comparsion Appendix B. T -stability of pullback-stable classes References