Related papers: Generalized edgewise subdivisions
In previous work, categories of algebras of endofunctors were shown to be enriched in categories of coalgebras of the same endofunctor, and the extra structure of that enrichment was used to define a generalization of inductive data types.…
In a step towards the classification of endotrivial modules for quasi-simple groups, we investigate endotrivial modules for the sporadic simple groups and their covers. A main outcome of our study is the existence of torsion endotrivial…
Functorial semi-norms are semi-normed refinements of functors such as singular (co)homology. We investigate how different types of representability affect the (non-)triviality of finite functorial semi-norms on certain functors or classes.…
The diagonal lemma asserts that if a map of bisimplicial sets is a levelwise weak equivalence in the Kan-Quillen model structure, then it induces a weak equivalence of the diagonal simplicial sets. In this short note, we observe that the…
Representing examples in a way that is compatible with the underlying classifier can greatly enhance the performance of a learning system. In this paper we investigate scalable techniques for inducing discriminative features by taking…
Generalizing the theory of parity sheaves on complex algebraic stacks due to Juteau-Mautner-Williamson, we develop a theory of twisted equivariant parity sheaves. We use this formalism to construct a modular incarnation of Lusztig and Yun's…
We introduce and analyze parallelizable algorithms to compress and accurately reconstruct finite simplicial complexes that have non-trivial automorphisms. The compressed data -- called a complex of groups -- amounts to a functor from (the…
In this paper we construct a cofibrantly generated model category structure on the category of all small symmetric multicategories enriched in simplicial sets.
In a previous work we proved the uniqueness and functoriality of primary unfoldings on simple Thom-Mather spaces, which is a functor to the category of smooth manifolds. In this article we extend these results for any stratified Thom-Mather…
We generalize the construction of reflection functors from classical representation theory of quivers to arbitrary small categories with freely attached sinks or sources. These reflection morphisms are shown to induce equivalences between…
We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the…
In this paper we introduce a notion of {\it generalized operad} containing as special cases various kinds of operad--like objects: ordinary, cyclic, modular, properads etc. We then construct inner cohomomorphism objects in their categories…
We show how one can do algebraic geometry with respect to the category of simplicial objects in an exact category. As a biproduct, we get a theory of derived analytic geometry.
We give a general construction of categorical idempotents which recovers the categorified Jones-Wenzl projectors, categorified Young symmetrizers, and other constructions as special cases. The construction is intimately tied to cell theory…
We outline the theory of reflections for prederivators, derivators and stable derivators. In order to parallel the classical theory valid for categories, we outline how reflections can be equivalently described as categories of fractions,…
In this article, we develop a general technique for gluing subcategories of $\infty$-categories. We obtain categorical equivalences between simplicial sets associated to certain multisimplicial sets. Such equivalences can be used to…
In this paper we propose unifying the categories of cochain complexes $\text{Ch}(\mathcal{C})$ and modules $\widehat{A}\text{-mod}$ over a repetitive algebra $\widehat{A}$. Motivated by their striking similarities and importance, we…
We introduce a very general extension of the monomorphism category as studied by Ringel and Schmidmeier which in particular covers generalised species over locally bounded quivers. We prove that analogues of the kernel and cokernel functor…
Given a simplicial idempotent augmented endofunctor $F$ on a simplicial combinatorial model category $M$, under the assumption of Vopenka's principle, we exhibit a set $A$ of cofibrant objects in $M$ such that $F$ is equivalent to $\CW_A$,…
If $X$ is a 2-Segal set, then the edgewise subdivision of $X$ admits a factorization system coming from upper and lower d\'ecalage. Using the correspondence between 2-Segal sets and unary operadic categories satisfying the blow-up axiom,…