**Speaker / Predavač**

Jovana Obradović, University of Novi Sad and University Paris Diderot, France

**Naslov / Title**

Weak cyclic Cat-operads

**Sažetak / Abstract**

The goal of this work is to establish the notion of weak cyclic Cat-operad, i.e. a cyclic operas enriched over a category Cat of small categories. This is done by weakening the axioms of cyclic operads, from equalities to natural isomorphisms, and by formulating conditions concerning these isomorphism which ensure coherence. This coherence is of the same kind as the coherence of symmetric monoidal categories: all diagrams made of associator and commutator isomorphisms are required to commute. However, in the setting of cyclic operads, where the existance of objects and morphisms depends on the shape of a fixed unrooted tree, these arrows do not always exist. In other words, the coherences that Mac Lane established for symmetric monoidal categories do not solve the coherence problem of weak cyclic Cat-operads. We shall exhibit the appropriate conditions of this setting and prove the coherence theorem.

vreme: sreda, 28.09.016. u 12:30

mesto: sala 305 (Nastavni blok, FTN)