We describe a Grothendieck construction for non-symmetric operads with values in categories, and hence in groupoids and posets. The construction produces a 2-category which is operadically fibered over the category Δ_s of finite non-empty ordinals and surjections. We describe an inverse for the construction, yielding an equivalence of constant-free non-symmetric categorical operads and operadic 2-categories (split-)fibered over Δ_s, which resembles the correspondence of categorical presheaves and fibered categories. The result provides a new characterization of non-symmetric categorical operads and tools to study them.
Keywords: Grothendieck construction; Categorical operad; Integration; Non-symmetric operad; 2-category; Operadic fibration
2020 MSC: 18D30;18M05;18M60;18N10
Theory and Applications of Categories, Vol. 45, 2026, No. 3, pp 130-150.
Published 2026-01-13.
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