Defines categorical homology via an Eilenberg-Steenrod analogue, proves a Dold-Kan correspondence using the Street nerve, and derives a Dold-Thom theorem for multiplicative structure and globe computations.
Duals and adjoints in higher Morita categories
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We study duals for objects and adjoints for $k$-morphisms in $\operatorname{Alg}_n(\mathcal{S})$, an $(\infty,n+N)$-category that models a higher Morita category for $E_n$ algebra objects in a symmetric monoidal $(\infty,N)$-category $\mathcal{S}$. Our model of $\operatorname{Alg}(\mathcal{S})$ uses the geometrically convenient framework of factorization algebras. The main result is that $\operatorname{Alg}_n(\mathcal{S})$ is fully $n$-dualizable, verifying a conjecture of Lurie. Moreover, we unpack the consequences for a natural class of fully extended topological field theories and explore $(n+1)$-dualizability.
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UNVERDICTED 2representative citing papers
Authors introduce a TFT-based framework for finite topological symmetries in QFT, including gauging, condensation defects, and duality defects, with an appendix on finite homotopy theories.
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Homology of higher categories
Defines categorical homology via an Eilenberg-Steenrod analogue, proves a Dold-Kan correspondence using the Street nerve, and derives a Dold-Thom theorem for multiplicative structure and globe computations.
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Topological symmetry in quantum field theory
Authors introduce a TFT-based framework for finite topological symmetries in QFT, including gauging, condensation defects, and duality defects, with an appendix on finite homotopy theories.