https://sfb-higher-invariants.app.uni-regensburg.de/index.php?action=history&feed=atom&title=The_root_functorThe root functor - Revision history2026-05-17T04:14:56ZRevision history for this page on the wikiMediaWiki 1.39.11https://sfb-higher-invariants.app.uni-regensburg.de/index.php?title=The_root_functor&diff=3133&oldid=prevCid36224: Created page with "Operads can be seen as a generalization of categories, where morphisms are allowed to have multiple inputs but still a single output. As oo-categories are designed to model ‘categories-up-to-homotopy’, the formalism of oo-operads serves to model ‘operads-up-to-homotopy’, where composition is defined only up to homotopy and higher coherence laws substitute equalities in the defining axioms. Many oo-operads arise from their strict counterparts by a process o..."2025-06-22T16:15:24Z<p>Created page with "Operads can be seen as a generalization of categories, where morphisms are allowed to have multiple inputs but still a single output. As oo-categories are designed to model ‘categories-up-to-homotopy’, the formalism of oo-operads serves to model ‘operads-up-to-homotopy’, where composition is defined only up to homotopy and higher coherence laws substitute equalities in the defining axioms. Many oo-operads arise from their strict counterparts by a process o..."</p>
<p><b>New page</b></p><div>Operads can be seen as a generalization of categories, where morphisms are allowed to have multiple inputs but still a single output. As oo-categories are designed to model ‘categories-up-to-homotopy’, the formalism of oo-operads serves to model ‘operads-up-to-homotopy’, where composition is defined only up to homotopy and higher coherence laws substitute equalities in the defining axioms. <br />
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Many oo-operads arise from their strict counterparts by a process of localization — that is, by formally inverting some specified set of arrows. This phenomenon is not new: by a well known result of Joyal, *every* oo-category is equivalent to the localization of a strict category. In this talk, I will extend this result, and by means of what I call 'the root functor' show that every oo-operad can be obtained as the localization of a strict operad, explicitly characterized. Essential to this will be the dendroidal formalism for oo-operads, where morphisms with multiple inputs are modeled by trees. As an application, I will deduce a characterization of the oo-category of algebras over an oo-operad as that of locally constant algebras over its strict resolution.</div>Cid36224