A note on connectedness in cartesian closed categories by Reino Vainio

“…In a separate Appendix we motivate the development of a homotopy theory for spaces of real-valued continuous maps endowed with the structure of continuous convergence.…”
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Homotopy methods for equations over finite fields by Lauder, A

“…This paper describes an application of some ideas from homotopy theory to the problem of computing the number of solutions to a multivariate polynomial equation over a finite field. …”

On CN-fibrations in bitopological semigroups by Dawood, Suliman, Kilicman, Adem

“…We extend the path lifting property in homotopy theory for topological spaces to bitopological semigroups and we show and prove its role in the CN-fibration property. …”
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On retracting properties and covering homotopy theorem for S-maps into Sχ-cofibrations and Sχ-fibrations by Amin Saif, Adem Kılıçman

“…In this paper we generalize the retracting property in homotopy theory for topological semigroups by introducing the notions of deformation S-retraction with its weaker forms and ES-homotopy extension property. …”
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Examples of Rational Toral Rank Complex by Toshihiro Yamaguchi

“…This is a combinatorial approach in rational homotopy theory.…”
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Derived equivalence for quantum symplectic resolutions by McGerty, K, Nevins, T

“…Using techniques from the homotopy theory of derived categories and noncommutative algebraic geometry, we establish a general theory of derived microlocalization for quantum symplectic resolutions. …”

A Model of Directed Graph Cofiber by Zachary McGuirk, Byungdo Park

“…In the homotopy theory of spaces, the image of a continuous map is contractible to a point in its cofiber. …”
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The quasitopos hull of the construct of closure spaces by Veerle Claes, G. Sonck

“…In the list of convenience properties for topological constructs the property of being a quasitopos is one of the most interesting ones for investigations in function spaces, differential calculus, functional analysis, homotopy theory, etc. The topological construct Cls of closure spaces and continuous maps is not a quasitopos. …”
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Some fixed point results via auxiliary functions on orthogonal metric spaces and application to homotopy by Nurcan Bilgili Gungor

“…On the other hand, homotopy theory constitute an important area of algebraic topology, but the application of fixed point results in orthogonal metric spaces to homotopy has not been done until now. …”
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Lifted generalized permutahedra and composition polynomials by Federico Ardila, Jeffrey Doker

“…We prove that this construction gives rise to Stasheff's multiplihedron from homotopy theory, and to the more general "nestomultiplihedra,'' answering two questions of Devadoss and Forcey. …”
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Generalized symmetries of topological field theories by Ben Gripaios, Oscar Randal-Williams, Joseph Tooby-Smith

“…Doing so allows many questions of physical interest to be answered using the tools of homotopy theory. We study both global and gauge symmetries, as well as ‘t Hooft anomalies, which we show fall into one of two classes. …”
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Torus actions, Morse homology, and the Hilbert scheme of points on affine space by Burt Totaro

“…We formulate a conjecture on actions of the multiplicative group in motivic homotopy theory. In short, if the multiplicative group G_m acts on a quasi-projective scheme U such that U is attracted as t approaches 0 in G_m to a closed subset Y in U, then the inclusion from Y to U should be an A^1-homotopy equivalence. …”
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On exact ∞-categories and the Theorem of the Heart by Barwick, Clark Edward

“…The new homotopy theory of exact∞-categories is introduced and employed to prove a Theorem of the Heart for algebraic K-theory (in the sense of Waldhausen). …”
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Multiplicative Structures on Algebraic K-Theory by Barwick, Clark, Barwick, Clark Edward

“…We therefore regard it as the stable homotopy theory of homotopy theories. In particular, it respects all algebraic structures, and as a result, we obtain the Deligne Conjecture for this form of $K$-theory.…”
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Spectral Fukaya Categories for Liouville Manifolds by Large, Tim

“…As a byproduct, we can generalize many familiar algebraic constructions in traditional Floer homology over the integers to Floer homotopy theory: among them symplectic cohomology, wrapped Floer cohomology, and the Donaldson-Fukaya category.…”
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On retracting properties and covering homotopy theorem for S-maps into Sχ-cofibrations and Sχ-fibrations by Saif, Amin, Kilicman, Adem

“…In this paper we generalize the retracting property in homotopy theory for topological semigroups by introducing the notions of deformation S-retraction with its weaker forms and EShomotopy extension property. …”
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Infinite symmetric products of rational algebras and spaces by Hu, Jiahao, Milivojević, Aleksandar

“…Applied to topology, we obtain a quick proof of the Dold–Thom theorem in rational homotopy theory for connected spaces of finite type. We also show that finite symmetric products of certain simple free graded-commutative algebras are free; this allows us to determine minimal Sullivan models for finite symmetric products of complex projective spaces.…”
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Simplicial quantum contextuality by Cihan Okay, Aziz Kharoof, Selman Ipek

“…We introduce a new framework for contextuality based on simplicial sets, combinatorial models of topological spaces that play a prominent role in modern homotopy theory. Our approach extends measurement scenarios to consist of spaces (rather than sets) of measurements and outcomes, and thereby generalizes nonsignaling distributions to simplicial distributions, which are distributions on spaces modeled by simplicial sets. …”
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Fixed Point Results in <inline-formula><math display="inline"><semantics><mi mathvariant="fraktur">F</mi></semantics></math></inline-formula>-Bipolar Metric Spaces with Application... by Badriah Alamri

“…Furthermore, the existence of the unique solution in homotopy theory is also investigated.…”
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Fixed-Point Results for Multi-Valued Mappings in Topological Vector Space-Valued Cone Metric Spaces with Applications by Hala Alzumi, Jamshaid Ahmad

“…As a demonstration of the applicability of our principal theorem, we prove a result in homotopy theory.…”
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