Related papers: External univalence for second-order generalized a…
This paper studies the homotopy theory of algebras and homotopy algebras over an operad. It provides an exhaustive description of their higher homotopical properties using the more general notion of morphisms called infinity-morphisms. The…
We prove that homotopy invariance and cancellation properties are satisfied by any linear category of correspondences that is defined, via Calm\`es and Fasel's construction, by an underlying cohomology theory. In particular, this includes…
Coherence theorems for covariant structures carried by a category have traditionally relied on the underlying term rewriting system of the structure being terminating and confluent. While this holds in a variety of cases, it is not a…
Our main result states that for each finite complex L the category ${\bf TOP}$ of topological spaces possesses a model category structure (in the sense of Quillen) whose weak equivalences are precisely maps which induce isomorphisms of all…
A class of structures is said to have the homomorphism-preservation property just in case every first-order formula that is preserved by homomorphisms on this class is equivalent to an existential-positive formula. It is known by a result…
Shulman's spatial type theory internalizes the modalities of Lawvere's axiomatic cohesion in a homotopy type theory, enabling many of the constructions from Schreiber's modal approach to differential cohomology to be carried out…
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…
Three philosophical principles are often quoted in connection with Leibniz: "objects sharing the same properties are the same object", "everything can possibly exist, unless it yields contradiction", "the ideal elements correctly determine…
We extend Lawvere-Pitts prop-categories (aka. hyperdoctrines) to develop a general framework for providing "algebraic" semantics for nonclassical first-order logics. This framework includes a natural notion of substitution, which allows…
Constructions of spectra from symmetric monoidal categories are typically functorial with respect to strict structure-preserving maps, but often the maps of interest are merely lax monoidal. We describe conditions under which one can…
We introduce the notion of a good map between topological spaces: a continuous map $f:X \to Y$ is *good* if for every non-empty irreducible locally closed subset $U \subseteq X$, there exists a non-empty open subset $W \subseteq Y$ such…
We give a new computation of Hochschild (co)homology of the exterior algebra, together with algebraic structures, by direct comparison with the symmetric algebra. The Hochschild cohomology is determined to be essentially the algebra of…
The usual homogeneous form of equality type in Martin-L\"of Type Theory contains identifications between elements of the same type. By contrast, the heterogeneous form of equality contains identifications between elements of possibly…
Working jointly in the equivalent categories of MV-al\-ge\-bras and lattice-ordered abelian groups with strong order unit (for short, unital $\ell$-groups), we prove that isomorphism is a sufficient condition for a separating subalgebra $A$…
In this paper we have found a necessary and sufficient condition for equivalence of two norms on a linear space using the theory of exponential vector space. Exponential vector space is an ordered algebraic structure which can be considered…
In a non-compact setting, the notion of hyperbolicity, and the associated structure of stable and unstable manifolds (for unbounded orbits), is highly dependent on the choice of metric used to define it. We consider the simplest version of…
We show that the Cantor-Schr\"oder-Bernstein Theorem for homotopy types, or $\infty$-groupoids holds in the following form: For any two types, if each one is embedded into the other, then they are equivalent. The argument is developed in…
E. Hrushovski proved tha the theory of difference-differential fields has a model companion. We prove this result and other maind properties of this theory that we call DCFA. We describe the SU rank a its relation with transcendence degree.…
Parametricity is a key metatheoretic property of type systems, which implies strong uniformity & modularity properties of the structure of types within systems possessing it. In recent years, various systems of dependent type theory have…
Constructing and manipulating homotopy types from categorical input data has been an important theme in algebraic topology for decades. Every category gives rise to a `classifying space', the geometric realization of the nerve. Up to weak…