Related papers: Yoneda Lemma for Elementary Higher Toposes

We first generalize a curve selection lemma for Noetherian schemes and apply it to prove a version of Curve Selection Lemma in arc spaces, answering affirmatively a question by Reguera. Furthermore, thanks to a structure theorem of…

We prove a flat strip theorem for 2-dimensional ptolemaic spaces.

We give a complete and careful proof of Quillen's theorem on the existence of the standard model category structure on the category of topological spaces. We do not assume any familiarity with model categories.

We give a complete and elementary proofs of "Jordan's sums" and study Euler's types sums. In particular we give a formula for the sum of series with same weight, which is similar to this one of classical 2-Euler's sums.

A duality of $\kappa$-normed topological vector spaces is defined and investigated. For such spaces the analog of the Mackey-Arens theorem is proved. There are investigated cases, when $\kappa$-normability of a topological vector space…

To each simplicial set $X$ we naturally assign an \'etendue ${\'E X}$ whose internal logic captures information about the geometry of $X$. In particular, we show that, for 'non-singular' objects $X$ and $Y$, the \'etendues ${\'E X}$ and…

In this note, the notion of cotorsion classes is introduced into the higher homological algebra. Our results motivate the definition, showing that this notion of $n$-cotorsion classes satisfies usual properties one could expect. In…

We prove sharp bounds for the equivalence of norms in tent spaces with respect to changes of angles. Some applications are given.

The aim of this paper is to give a proof of improving of Zalcman's lemma.

We develop the theory of topoi internal to an arbitrary $\infty$-topos $\mathcal B$. We provide several characterisations of these, including an internal analogue of Lurie's characterisation of $\infty$-topoi, but also a description in…

In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.

A lattice $\Lambda$ is said to be an extension of a sublattice $L$ of smaller rank if $L$ is equal to the intersection of $\Lambda$ with the subspace spanned by $L$. The goal of this paper is to initiate a systematic study of the geometry…

We prove two completeness results for Kleene algebra with tests and a top element, with respect to guarded string languages and binary relations. While the equational theories of those two classes of models coincide over the signature of…

We give another proof of Toyoda's theorem that describes 5-point subpaces in CAT(0) length spaces

We prove that several results of lineability/spaceability in the framework of sequence spaces are valid in a stricter sense.

We present elementary proofs of weighted embedding theorems for radial potential spaces and some generalizations of Ni's and Strauss' inequalities in this setting.

We formulate and prove a general result in spirit of hypergraph removal lemma for measurable functions of several variables.

We generalize Bulitko's Lemma to equations over (or homomorphisms into) groups that have $\kappa$-acylindrical splittings.

We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.

We show that H-spaces with finitely generated cohomology, as an algebra or as an algebra over the Steenrod algebra, have homotopy exponents at all primes. This provides a positive answer to a question of Stanley.