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Is there a name for an $\infty$-category C that admits a zero object and suspensions such that the suspension functor $C \to C$ is an equivalence but which does not necessarily admit cofibers and fibe …

Let $\mathcal{C}$ be a combinatorial model category and $\mathrm{T}$ a monad on $\mathcal{C}.$ Assume that the model structure on $\mathcal{C}$ lifts to a model structure on the category of $\math …

Is every symmetric monoidal combinatorial model category symmetric monoidally Quillen equivalent (by a zig-zag of symmetric monoidal Quillen equivalences) to a symmetric monoidal combinatorial simpli …

Let $\mathrm{K}$ be a field of char. 0. Given a chain complex $\mathrm{X} $ over $\mathrm{K}$ denote $\mathrm{E}(\mathrm{X})$ the co-square-zero-extension on $\mathrm{X}, $ i.e. the cocommutative no …