Related papers: On generalized equilogical spaces
In this paper, we unify various approaches to generalized covering space theory by introducing a categorical framework in which coverings are defined purely in terms of unique lifting properties. For each category $\mathcal{C}$ of…
We provide a general construction of induced $t$-structures, that generalizes standard $t$-structures for $\infty$-categories of sheaves. More precisely, given a presentable $\infty$-category $\mathcal{X}$ and a presentable stable…
The notion of a proper Ellis semigroup compactification is introduced. Ellis's functional approach shows how to obtain them from totally bounded equiuniformities on a phase space $X$ when the acting group $G$ is with the topology of…
The elementary quotient completion of an elementary doctrine in the sense of Lawvere was introduced in previous work by the first and third authors. It generalises the exact completion of a category with finite products and weak equalisers.…
We use Kan injectivity to axiomatise concepts in the 2-category of topoi. We showcase the expressivity of this language through many examples, and we establish some aspects of the formal theory of Kan extension in this 2-category (pointwise…
A general method for lifting weak factorization systems in a category S to model category structures on simplicial objects in S is described, analogously to the lifting of cotorsion pairs in Abelian categories to model category structures…
After two papers on weak cubical categories and {\it collarable} cospans, respectively, we put things together and construct a {\it weak} cubical category of cubical {\it collared} cospans of topological spaces. We also build a second…
We study the relationship between presheaf constructions and free cocompletions in the context of formal category theory, elucidating the coincidence between the two concepts in familiar settings. We show that, in a virtual equipment…
Quillen defined a {\em model category} to be a category with finite limits and colimits carrying a certain extra structure. In this paper, we show that only finite products and coproducts (in addition to the certain extra structure alluded…
Let G be a discrete group. We give methods to compute for a generalized (co-)homology theory its values on the Borel construction (EG x X)/G of a proper G-CW-complex X satisfying certain finiteness conditions. In particular we give formulas…
We give a general framework of equivariant model category theory. Our groups G, called Hopf groups, are suitably defined group objects in any well-behaved symmetric monoidal category V. For any V, a discrete group G gives a Hopf group,…
We develop a constructive model of homotopy type theory in a Quillen model category that classically presents the usual homotopy theory of spaces. Our model is based on presheaves over the cartesian cube category, a well-behaved…
Let $X$ be a variety with an action by an algebraic group $G$. In this paper we discuss various properties of $G$-equivariant $D$-modules on $X$, such as the decompositions of their global sections as representations of $G$ (when $G$ is…
In our previous paper [9], we have introduced topological nearly entropy, Ent_N (f) by restricting X into a class of nearly compact spaces. In the present paper, some additional properties of this notion are studied. Furthermore, we…
Let $X$ be a $G$-space. In this paper, we introduce the notion of sectional category with respect to $G$. As a result, we obtain $G$-homotopy invariants: the LS category with respect to $G$, the sequential topological complexity with…
In fairly elementary terms this paper presents, and expands upon, a recent result by Garner by which the notion of topologicity of a concrete functor is subsumed under the concept of total cocompleteness of enriched category theory.…
We propose the notion of a supercategory as an alternative approach to supermathematics. We show that this setting is rich to carry out many of the basic constructions of supermathematics. We also prove generalizations of a number of…
For a smooth spacetime $X$, based on the timelike homotopy classes of its timelike paths, we define a topology on $X$ that refines the Alexandrov topology and always coincides with the manifold topology. The space of timelike or causal…
Given a symmetric monoidal category $C$ with product $\sqcup$, where the neutral element for the product is an initial object, we consider the poset of $\sqcup$-complemented subobjects of a given object $X$. When this poset has finite…
For any length category, we establish a set of rules (necessary and sufficient) that ensure a partial order on the isomorphism classes of simple objects such that the category is equivalent to the category of finite dimensional…