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Variations on the notions of Reedy model structures and projective model structures on categories of diagrams in a model category are introduced. These allow one to choose only a subset of the entries when defining weak equivalences, or to use different model categories at different entries of the diagrams. As a result, a bisimplicial model category that can be used to recover the algebraic K-theory for any Waldhausen subcategory of a model category is produced.
We construct and study projective and Reedy model category structures for bimodules and infinitesimal bimodules over topological operads. Both model structures produce the same homotopy categories. For the model categories in question, we build expli
We present a family of model structures on the category of multicomplexes. There is a cofibrantly generated model structure in which the weak equivalences are the morphisms inducing an isomorphism at a fixed stage of an associated spectral sequence.
The missing mass problem has not been solved decisively yet. Observations show that if gravity is to be modified, then the MOND theory is its excellent approximation on galactic scales. MOND suggests an adjustments of the laws of physics in the limit
In several experiments involving material background, it has been observed that the Chu, Einstein-Laub and Ampere formulations of optical force lead to either different optical forces or wrong total optical force. In order to identify the exact reaso
We initiate the study of model structures on (categories induced by) lattice posets, a subject we dub homotopical combinatorics. In the case of a finite total order $[n]$, we enumerate all model structures, exhibiting a rich combinatorial structure e