Idempotents in intensional type theory by Michael Shulman

“…Both proofs are inspired by parallel results of Lurie in higher category theory, showing that ideas from higher category theory and homotopy theory can have applications even in ordinary MLTT. …”
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Topological Interactions Between Homotopy and Dehn Twist Varieties by Susmit Bagchi

“…The interplay between homotopy theory and Dehn twists exposes a rich set of properties. …”
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Cogroupoid structures on the circle and the Hodge degeneration by Tasos Moulinos

“…In particular, we relate the existence of nontrivial Todd classes for schemes to the failure of the pinch map to be formal in the sense of rational homotopy theory. Finally, we record some consequences of this bit of structure at the level of Hochschild cohomology.…”
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Scalable spaces by Berdnikov, Aleksandr, Manin, Fedor

“…They are also characterized by particularly nice behavior from the point of view of quantitative homotopy theory. Among other results, we show that spaces which are formal but not scalable provide counterexamples to Gromov’s long-standing conjecture on distortion in higher homotopy groups.…”
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Number of Compatible Pair for Nontrivial Actions of Finite Cyclic 2-Groups by Sahimel Azwal, Sulaiman, Mohd Sham, Mohamad, Yuhani, Yusof, Mohammed Khalid, Shahoodh

“…The nonabelian tensor product of groups has its origins in the algebraic K-theory and homotopy theory. The nonabelian tensor product for a pair of groups is defined when the action act compatibly on each other. …”
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Fixed-point results via $ \alpha_{i}^{j} $-$ \left({\bf D}_{{\mathscr{C}}}\left(\mathfrak{P}_{\hat E}\right)\right) $-contractions in partial $ \flat $-metric spaces by Leyla Sağ Dönmez, Abdurrahman Büyükkaya, Mahpeyker Öztürk

“…Additionally, the efficiency of the result of this study is demonstrated through some examples and an application to homotopy theory.…”
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Some common fixed point theorems in bipolar metric spaces and applications by Joginder Paul, Mohammad Sajid, Naveen Chandra, Umesh Chandra Gairola

“…In addition, we provide some examples to illustrate our theorems, and applications are obtained in areas of homotopy theory and integral equations by using iterative methods for mathematical operators on a bipolar metric space.…”
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Dirac geometry II: coherent cohomology by Lars Hesselholt, Piotr Pstrągowski

“…We apply the general theory to stable homotopy theory and use Quillen’s theorem on complex cobordism and Milnor’s theorem on the dual Steenrod algebra to identify the Dirac stacks corresponding to $\operatorname {MU}$ and $\mathbb {F}_p$ in terms of their functors of points. …”
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A Constructive Treatment to Elemental Life Forms through Mathematical Philosophy by Susmit Bagchi

“…The formalisms of predicate logic, probabilistic inference and homotopy theory of algebraic topology are employed to construct a structure in local time-scale horizon and in cosmological time-scale horizon. …”
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The Sierpinski Object in the Scott Realizability Topos by Tom de Jong, Jaap van Oosten

“…In the last section we build a model for homotopy theory, where the order-discrete objects are exactly those objects which only have constant paths.…”
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The Number of Compatible Pair of Actions for Cyclic Groups of 2-Power Order by Sahimel Azwal, Sulaiman, Yuhani, Yusof, Shahoodh, Mohammed Khalid

“…The non-abelian tensor product of groups has its origins in the algebraic K-theory and homotopy theory. The nonabelian tensor product for a pair of groups is defined when the actions act compatibly on each other. …”
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Compatible actions for finite cyclic groups of p-power order by Shahoodh, Mohammed Khalid

“…The concept of the nonabelian tensor product of groups has its origins in the algebraic K-theory and the homotopy theory. This concept is defined on the actions which are compatible to each other. …”
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The Discrete Fundamental Group of the Associahedron by Christopher Severs, Jacob White

“…We approach the associahedron from the point of view of discrete homotopy theory, that is we consider 5-cycles in the 1-skeleton of the associahedron to be combinatorial holes, but 4-cycles to be contractible. …”
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Knot topology of exceptional point and non-Hermitian no-go theorem by Haiping Hu, Shikang Sun, Shu Chen

“…In this Letter, we provide a topological classification of isolated EPs based on homotopy theory. In particular, the classification indicates that an nth order EP in two dimensions is fully characterized by the braid group B_{n}, with its eigenenergies tied up into a geometric knot along a closed path enclosing the EP. …”
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Maps and localizations in the category of Segal spaces by Robinson, Hugh Michael, 1978-

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The generalized Tate construction by Stroilova, Olga (Olga Y.)

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Discrete Morse theory and classifying spaces by Nanda, V, Tamaki, D, Tanaka, K

“…It is shown that the classifying space of is homotopy equivalent to X by using homotopy theory of 2-categories. This result can be also regarded as a discrete analogue of the unpublished work of Cohen, Jones, and Segal on Morse theory in early 90's.…”

Tame Topology by Artur Piękosz

“…The language of smopologies and bounded continuous mappings simplifies the language of certain Grothendieck sites and permits us to glue together infinite families of definable sets in structures with topologies, which was important when developing the o-minimal homotopy theory.…”
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The Toulouse–Kleman homotopic classification of topological defects in ordered systems illustrated by experiments by Pieranski, Pawel, Godinho, Maria Helena

“…Classification of defects in ordered systems, based on the homotopy theory, conceived by Gérard Toulouse and Maurice Kléman has a very wide range of applications. …”
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Localization at b₁₀ in the stable category of comodules over the Steenrod reduced powers by Belmont, Eva Kinoshita

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