On Homotopy Invariance for Algebras over Colored Props
نویسنده
چکیده
Over a monoidal model category, under some mild assumptions, we equip the categories of colored PROPs and their algebras with projective model category structures. A BoardmanVogt style homotopy invariance result about algebras over cofibrant colored PROPs is proved. As an example, we define homotopy topological conformal field theories and observe that such structures are homotopy invariant.
منابع مشابه
Props in Model Categories and Homotopy Invariance of Structures
We prove that any category of props in a symmetric monoidal model category inherits a model structure. We devote an appendix, about half the size of the paper, to the proof of the model category axioms in a general setting. We need the general argument to address the case of props in topological spaces and dg-modules over an arbitrary ring, but we give a less technical proof which applies to th...
متن کاملAcademy of Sciences of the Czech Republic Mathematical Institute Operads and Props
We review definitions and basic properties of operads, PROPs and algebras over these structures. Dedicated to the memory of Jakub Jan Ryba (1765–1815) Operads involve an abstraction of the family {Map(X, X)}n≥0 of composable functions of several variables together with an action of permutations of variables. As such, they were originally studied as a tool in homotopy theory, specifically for it...
متن کاملOperads and Props
We review definitions and basic properties of operads, PROPs and algebras over these structures. Dedicated to the memory of Jakub Jan Ryba (1765–1815) Operads involve an abstraction of the family {Map(X, X)}n≥0 of composable functions of several variables together with an action of permutations of variables. As such, they were originally studied as a tool in homotopy theory, specifically for it...
متن کاملHigher Dimensional Algebras via Colored Props
Starting from any unital colored PROP P, we define a category P(P) of shapes called P-propertopes. Presheaves on P(P) are called P-propertopic sets. For 0 ≤ n ≤ ∞ we define and study n-time categorified P-algebras as P-propertopic sets with some lifting properties. Taking appropriate PROPs P, we obtain higher categorical versions of polycategories, 2-fold monoidal categories, topological quantu...
متن کامل2 1 Ja n 20 02 HOMOTOPY INVARIANCE OF AF - EMBEDDABILITY
We prove that AF-embeddability is a homotopy invariant in the class of separable exact C∗-algebras. This work was inspired by Spielberg’s work on homotopy invariance of AFembeddability and Dadarlat’s serial works on AF-embeddability of residually finite dimensional C∗-algebras.
متن کامل