## TQFT as a generalization of spherical homology

Speculating about the question posed in the end of this confused post I recognised, that the generalization involved makes some sense. Spherical homology is generalised in two directions. Firstly 2-sphere is replaced with any compact oriented 2-manifold. Secondly a BV (f2-)algebra is replaced with a cyclic 2-category. As a result one get a structure that strongly reminds TQFT up to decorations. By decorations I mean metric, counit and so on. This conjectural structure plays for cyclic 2-categories the same role as Hochschild homology plays for (1-)categories.

## Homotopy cyclic 2-category

In the paper “What do DG categories form?” D. Tamarkin introduced the notion of a homotopy 2-category. Its important feature is that for any object on the operad of chains of little discs acts. Below a notion of homotopy cyclic 2-category is introduced. For it the complex is acted by the operad of chains of *framed* little discs.

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