Classifying spaces of categories and term rewriting.
Classifying toposes and foliations
For any etale topological groupoid (for example, the holonomy groupoid of a foliation), it is shown that its classifying topos is homotopy equivalent to its classifying space. As an application, we prove that the fundamental group of Haefliger for the (leaf space of) a foliation agrees with the one introduced by Van Est. We also give a new proof of Segal’s theorem on Haefliger’s classifying space .
Clones, coclones and coconnected spaces.
Closed categories and Banach spaces
Closed categories and topological vector spaces
Closedness properties of internal relations. I. A unified approach to Mal'tsev, unital and subtractive categories.
Closedness properties of internal relations. II: Bourn localization.
Closedness properties of internal relations. IV: Expressing additivity of a category via subtractivity.
Closure operators in exact completions.
Closure operators, monomorphisms and epimorphisms in categories of groups
Closure operators on O-categories.
Cluster categories for algebras of global dimension 2 and quivers with potential
Let be a field and a finite-dimensional -algebra of global dimension . We construct a triangulated category associated to which, if is hereditary, is triangle equivalent to the cluster category of . When is Hom-finite, we prove that it is 2-CY and endowed with a canonical cluster-tilting object. This new class of categories contains some of the stable categories of modules over a preprojective algebra studied by Geiss-Leclerc-Schröer and by Buan-Iyama-Reiten-Scott. Our results also...
Cluster characters for 2-Calabi–Yau triangulated categories
Starting from an arbitrary cluster-tilting object in a 2-Calabi–Yau triangulated category over an algebraically closed field, as in the setting of Keller and Reiten, we define, for each object , a fraction using a formula proposed by Caldero and Keller. We show that the map taking to is a cluster character, i.e. that it satisfies a certain multiplication formula. We deduce that it induces a bijection, in the finite and the acyclic case, between the indecomposable rigid objects of the cluster...
Coactions and fell bundles.
Coalgebras, braidings, and distributive laws.
Coarse dimensions and partitions of unity.
Gromov and Dranishnikov introduced asymptotic and coarse dimensions of proper metric spaces via quite different ways. We define coarse and asymptotic dimension of all metric spaces in a unified manner and we investigate relationships between them generalizing results of Dranishnikov and Dranishnikov-Keesling-Uspienskij.
Coarse structures and group actions
The main results of the paper are: Proposition 0.1. A group G acting coarsely on a coarse space (X,𝓒) induces a coarse equivalence g ↦ g·x₀ from G to X for any x₀ ∈ X. Theorem 0.2. Two coarse structures 𝓒₁ and 𝓒₂ on the same set X are equivalent if the following conditions are satisfied: (1) Bounded sets in 𝓒₁ are identical with bounded sets in 𝓒₂. (2) There is a coarse action ϕ₁ of a group G₁ on (X,𝓒₁) and a coarse action ϕ₂ of a...
Cochain operations and subspace arrangements.
Cochains and homotopy type
Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E∞ algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of E∞ algebras is faithful but not full.
Cocordance and Isotopy of Smooth Embeddings in Low Codimensions.