The purpose of this paper is two-fold. In Part 1 we introduce a new theory of operadic categories and their operads. This theory is, in our opinion, of an independent value. In Part 2 we use this new theory together with our previous results to prove that multiplicative 1-operads in duoidal categories admit, under some mild conditions on the underlying monoidal category, natural actions of contractible 2-operads. The result of D. Tamarkin on the structure of dg-categories, as well as the classical Deligne conjecture for the Hochschild cohomology, is a particular case of this statement.
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机译：本文的目的是双重的。在第1部分中，我们介绍了一种新的操作符类别及其操作符理论。我们认为，该理论具有独立的价值。在第2部分中，我们使用这一新理论以及我们先前的结果来证明，在基本单调类别的某些温和条件下，双曲面类别的乘法1-operads承认可收缩的2-operads的自然作用。 D. Tamarkin关于dg类结构的结果，以及Hochschild同调的经典Deligne猜想，就是这种说法的一个特例。
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