cyclic space in nLab
A cyclic space is a cyclic object in a category of spaces, usually in one of the standard presentations of homotopy types, hence in ...
The cyclic loop space ℒ X ⫽ S 1 \mathcal{L}X \sslash S^1 is equivalently the right base change/dependent product along the canonical point ...
A vector — hence an element of some vector space ℋ \mathcal{H} — is called cyclic with respect to the action/representation of some algebra ...
Hochschild homology may be understood as the cohomology of free loop space objects (as described there). These free loop space objects are ...
A cyclic set is a presheaf on the cyclic category (which is often called Connes' cyclic category though it is cocyclic, with the usual contravariant confusion)
The concept of cyclic object is the generalization of that of cyclic sets where Set may be replaced with any other category. Cyclic objects are ...
2. Properties ... A free loop space, ℒ X \mathcal{L} X , is a cyclotomic space, where S 1 S^1 acts by rotation of loops. Let R X = holim R r ρ r * ...
For a discrete group G, BG is, roughly speaking, a path-connected topological space X such that the fundamental group of X is isomorphic to G and the higher ...
The cycle category is a generalized Reedy category (see Berger-Moerdijk 08, example 2.7). Hence “cyclic spaces” carry a generalized Reedy model ...
An epicyclic category is certain small category containing the cyclic category; it has been introduced by Thomas Goodwillie (in an unpublished ...
What non-categorical applications are there of homotopical algebra?
There is a topological operad called "the splicing operad" that acts on embedding spaces. It acts on a space closely related to the space of ...
Realization of Cyclic Spaces - Julius Plenz - Blog
What changes is that for an s-cyclic space X•, PaX• carries a Cas ... The nLab (http://ncatlab.org) also provided interesting examples and ...
The homotopy quotient by that action ℒ ( X ) / S 1 \mathcal{L}(X)/S^1 (the “cyclic loop space”) contains what is known as the twisted loop space ...
nLab -- General Discussion | The n-Category Café - Welcome
One of the aims of the nLab is to provide a space for collaborative work to take place. ... I mean if cycle category for cyclic homology ...
Eilenberg–MacLane space - Wikipedia
In mathematics, specifically algebraic topology, an Eilenberg–MacLane space is a topological space with a single nontrivial homotopy group.
completion of normed vector space in category theory
It's mentioned in the nLab page https://ncatlab.org/nlab/show/completion but how about the detailed proof ? Below I attached the definition ...
nLab > Latest Changes: cyclic space ... it seems this entry was missing among cycle category, cyclic object and cyclotomic spectrum. Am starting something, but ...
Help me gain some intuition for the simplex category
The augmented simplicity category Δa is defined to have all finite ordinal as its objects, and order preserving maps as its morphisms. nLab ...
In linear algebra, cycles are strings of linearly independent vectors obtained by applying increasing powers of an operator to a single vector; cyclic subspaces ...
The mLab - Composable adjunction
Definition: co-right pushouts are said to be closed provided that co-extensions over the cover of endofunctors are "vector space-like" from T's point of view.