Simplicial homotopy theory

Foundations of Algebraic Topology

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Homotopical Algebra

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Reduced Product Spaces

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The Geometric Realization of a Semi-Simplicial Complex

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Homologie nicht-additiver Funktoren. Anwendungen

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On the structure and applications of the steenrod algebra

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ON THE COBAR CONSTRUCTION

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A triangulation criterion

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3-Crossed Modules of Commutative AlgebrasPreprint

Kuzpınarı, T. S., Odabaş, A., & Uslu, E. Ö. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1003.0985 · Cited by 2

Foliated norms on fundamental group and homologyPreprint

Kuessner, T. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0303234 · Cited by 2

Loop spaces and homotopy operations

Blanc, D. A. (1997) · Fundamenta Mathematicae · doi:10.4064/fm-154-1-75-95 · Cited by 2

An extension theory for partial groupsPreprint

Broto, C., & González, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2105.03457 · Cited by 2

A new quantum computational set-up for algebraic topology via simplicial sets

Zucchini, R. (2025) · Journal of AppliedMath · doi:10.59400/jam3011 · Cited by 1

Simplicial approximation

Jardine, J. F. (2004) · Theory and applications of categories · doi:10.70930/tac/wwsvkzot · Cited by 1

On the simplicial structure of uncertain information

Martínez‐Moreno, J., & Zamora, D. G. (2026) · Computational and Applied Mathematics · doi:10.1007/s40314-026-03885-0 · Cited by 1

Some Relations Between Crossed Modules and Simplicial Objects in Categories of Interest

Boyacı, Y., & Avcıoğlu, O. (2014) · European Journal of Pure and Applied Mathematics · Cited by 1

Relations between simplicial groups, 3-crossed modules and 2-quadratic modules

Ati̇k, H., & Ulualan, E. (2014) · Acta Mathematica Sinica English Series · doi:10.1007/s10114-014-3416-9 · Cited by 1

On Baer invariants of pairs of groups

Mashayekhy, B., Mırebrahımı, H., & Vasagh, Z. (2016) · Georgian Mathematical Journal · doi:10.1515/gmj-2016-0067 · Cited by 1

Nonabelian H1 and the Étale Van Kampen Theorem

Misamore, M. D. (2011) · Canadian Journal of Mathematics · doi:10.4153/cjm-2011-030-x · Cited by 1

On Kan Fibrations for Maltsev Algebras

Jibladze, M., & Pirashvili, T. (2002) · Georgian Mathematical Journal · doi:10.1515/gmj.2002.71 · Cited by 1

The simplicial coalgebra of chains determines homotopy types rationally and one prime at a time

Rivera, M., Wierstra, F., & Zeinalian, M. (2021) · Transactions of the American Mathematical Society · doi:10.1090/tran/8579 · Cited by 1

The uniform homotopy category

Krishnan, S., & Ogle, C. (2023) · Journal of Pure and Applied Algebra · doi:10.1016/j.jpaa.2023.107425 · Cited by 1

The Twisted Homology of Simplicial Set

Zhang, M. M., Li, J. Y., & Wu, J. (2022) · Acta Mathematica Sinica English Series · doi:10.1007/s10114-022-2190-3 · Cited by 1

λ-ring structures on the K-theory of algebraic stacks

Joshua⋆, R., & Pelaez, P. (2024) · Annals of K-Theory · doi:10.2140/akt.2024.9.519 · Cited by 1

Piecewise Linear Bundles in the Metastable Range

Millett, K. C. (1976) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1976-0423361-7 · Cited by 1

HOMOLOGY OF LIE ALGEBRAS WITH Λ/qΛ COEFFICIENTS AND EXACT SEQUENCES

Khmaladze, E. (2002) · Cited by 1

Peiffer Commutators by Using GAP Package

Mutlu, A. (1998) · Mathematical and Computational Applications · doi:10.3390/mca3010059 · Cited by 1

Loop space homology of a small category

Broto, C., Levi, R., & Oliver, B. (2021) · Annals of K-Theory · doi:10.2140/akt.2021.6.425 · Cited by 2

Algebraic EHP Sequences Revisited

Cuong, N. T. (2018) · Proceedings of the Edinburgh Mathematical Society · doi:10.1017/s0013091518000652 · Cited by 1

A simple proof of Curtis’ connectivity theorem for Lie powers

Ivanov, S. O., Romanovskii, V., & Semenov, A. (2020) · Homology Homotopy and Applications · doi:10.4310/hha.2020.v22.n2.a15 · Cited by 1

Generalized Homotopy in C- Categories

Machín, S. R., Díaz, F. J. D., & Remedios, J. (2001) · Dialnet (Universidad de la Rioja) · Cited by 1

On Baer Invariants of Pairs of GroupsPreprint

Vasagh, Z., Mırebrahımı, H., & Mashayekhy, B. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1106.1278 · Cited by 1

The functors Wbar and Diag o Nerve are simplicially homotopy equivalentPreprint

Thomas, S. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0804.1082 · Cited by 1

A Combinatorial Definition of n-Types of Simplicial Commutative Algebras

ARAVASI, Z., & M., M. K. A. (1998) · DergiPark (Istanbul University) · Cited by 1

Localitzacions i complecions d'espais anesfèrics

Bastardas, G. (2003) · TDX (Tesis Doctorals en Xarxa) · Cited by 1

Enumerating prime-power homotopy k-types

Ellis, G. J. (1999) · Mathematische Zeitschrift · doi:10.1007/pl00004760 · Cited by 1

Classifying spectra for generalized homology theories

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An intrinsic construction of steenrod squares for mod 2 de Rham forms

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On Schur Multipliers of Pairs and Triples of Groups with Topological ApproachPreprint

Mırebrahımı, H., & Mashayekhy, B. (2011) · arXiv (Cornell University) · doi:10.7508/ijmsi.2011.02.006 · Cited by 1

Cochain operations and subspace arrangements.

Klaus, S. (2003) · Cited by 1

Simplicial cochain algebras for diffeological spaces

Kuribayashi, K. (2019) · SOAR (Shinshu University) · doi:10.48550/arxiv.1902.10937 · Cited by 1

Self-derived localizations of groupsPreprint

Akhtiamov, D., Ivanov, S. O., & Pavutnitskiy, F. (2019) · arXiv (Cornell University) · Cited by 1

Cubical approximation for directed topology IPreprint

Krishnan, S. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1012.0509 · Cited by 1

Iterated suspensions are coalgebras over the little disks operadPreprint

Moreno-Fernández, J. M., & Wierstra, F. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1909.11043 · Cited by 1

A Unified Topological Approach to Data SciencePreprint

Grbić, J., Wu, J., Xia, K., & Wei, G. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2103.16926 · Cited by 1

Adams representability in triangulated categories

Raventós, O. (2011) · TDX (Tesis Doctorals en Xarxa) · Cited by 1

Enriched functor categories

Schwede, S. (2018) · doi:10.1017/9781108349161.010 · Cited by 1

Introduction

Morel, F. (2012) · Lecture notes in mathematics · doi:10.1007/978-3-642-29514-0_1 · Cited by 1

Rational Models of the Complement of a Subpolyhedron in a Manifold with Boundary

Bulens, H. C., Lambrechts, P., & Stanley, D. (2017) · Canadian Journal of Mathematics · doi:10.4153/cjm-2017-021-3

A TOPOLOGICAL APPROACH TO THE NILPOTENT MULTIPLIERS

Vasagh, Z., Mashayekhy, B., & Hanieh (2013)

On the Λ-algebra and the homology of symmetric groups

Singer, W. M. (1987) · Lecture notes in mathematics · doi:10.1007/bfb0078749

Some Properties of Finitely Presented Groups with Topological ViewpointsPreprint

Mashayekhy, B., & Mırebrahımı, H. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1012.1744

Infinite dimensional manifolds from a new point of viewPreprint

Lin, X. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1012.5885

On Combinatorial Descriptions of Homotopy Groups of $ΣK(π,1)$Preprint

Wu, J. (1995) · arXiv (Cornell University) · doi:10.48550/arxiv.math/9508217

Some Properties of Finitely Presented Groups with Topological Viewpoints

Fard, B. M., & Paziquee, B. H. M. (2010)

Une suite spectrale pour les groupes d'homotopie des espaces d'applications équivariantes

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Reflection simplicial maps and group cohomology

Klaus, S. (2009) · Note di matematica/Note di matematica - Università degli studi di Lecce · doi:10.1285/i15900932v26n1p1

Abelian Groups in omega-categoriesPreprint

Milburn, B. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1106.5434

Un acercamiento algebraico a la teoría de Torres de Postnikov

Muñoz, M. Á. G. (2003)

On degree of simplicial homomorphisms between link groups

Li, F. (2013) · Topology and its Applications · doi:10.1016/j.topol.2013.10.026

Book Review: Combinatorial homotopy and {\rm {4}}-dimensional complexes

Harper, J. R. (1993) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-1993-00375-6

The E. H. P. spectral sequence

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Simplicial Schreier Systems and the Commutator Subgroup of the Free Group on the Circle

Ghullam, S. A. (1978) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-1978-0507217-4

Decompositions of loop spaces Ω(X∨Y∨Z) : A combinatorial approach

Weng, W., & Shen, W. (2009) · Topology and its Applications · doi:10.1016/j.topol.2009.04.018

on the Baer Invariants of Triples of Groups

Vasagh (2012) · Journal of Advanced Research in Pure Mathematics · doi:10.5373/jarpm.1160.102311

Combinatorial proofs of the Lambda algebra basis and EHP sequence

Richter, W. (2009) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-09-09763-9

Book Review: Simplicial homotopy theory

Gray, B. (2000) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-00-00895-8

Nerves of Trigroupoids as Duskin-Glenn’s 3-Hypergroupoids

Carrasco, P. (2014) · Applied Categorical Structures · doi:10.1007/s10485-014-9374-7

Simplicial monoid actions and associated monoid constructions

Gao, M., & Wu, J. (2015) · Journal of Homotopy and Related Structures · doi:10.1007/s40062-015-0102-2

Homotopy of profinite groupsPreprint

Mikhovich, A. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1205.4365

Unramified Sheaves and Strongly $${\mathbb{A}}^{1}$$ -Invariant Sheaves

Morel, F. (2012) · Lecture notes in mathematics · doi:10.1007/978-3-642-29514-0_2

Homotopy types of reduced 2-nilpotent simplicial groupsPreprint

Baues, H.-J., & Mikhailov, R. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0804.2000

Bachelor Thesis in Mathematics

Johansen, R. N. (2012)

The Affine B.G. Property for the Linear Groups and the Grassmanian

Morel, F. (2012) · Lecture notes in mathematics · doi:10.1007/978-3-642-29514-0_9

OF A WEDGE

Hirschhorn, P. (2016)

A New Translation Between Two Complexes

Khosravi, H., & Golmakani, H. (2012)

On Profinite Simplicial Groups

AYTEKİN, A. (2010)

Minimality in diagrams of simplicial sets

Broto, C., Flores, R., & Giraldo, C. (2019) · Journal of Homotopy and Related Structures · doi:10.1007/s40062-019-00239-y

$${\mathbb{A}}^{1}$$ -Homotopy Sheaves and $${\mathbb{A}}^{1}$$ -Homology Sheaves

Morel, F. (2012) · Lecture notes in mathematics · doi:10.1007/978-3-642-29514-0_6

ℰn–Hopf invariants

Wierstra, F. (2020) · Algebraic & Geometric Topology · doi:10.2140/agt.2020.20.2905

Some Properties of the Schur Multiplier with Algebraic Topological Approach

Fard, B. M., & Paziquee, B. H. M. (2008)

Infinite dimensional manifolds from a new point of view

Lin, X. (2012) · Topology and its Applications · doi:10.1016/j.topol.2012.07.018

Realization of a Lie algebra and classifying space of crossed modulesPreprint

Félix, Y., & Tanré, D. (2021) · arXiv (Cornell University)

Global stable homotopy theory

Schwede, S. (2018) · Stefan Schwede eBooks · doi:10.1017/9781108349161.005

Global Thom and K-theory spectra

Schwede, S. (2018) · Stefan Schwede eBooks · doi:10.1017/9781108349161.007

When are two spaces homotopy equivalent?Preprint

Šimková, M. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2105.10443

Realization of Lie algebras and classifying spaces of crossed modules

Félix, Y., & Tanré, D. (2024) · Algebraic & Geometric Topology · doi:10.2140/agt.2024.24.141

Simplicial-like Identities for The Paths and The Regular Paths on Discrete SetsPreprint

Ren, S. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2107.09868

Index of symbols

Schwede, S. (2018) · Stefan Schwede eBooks · doi:10.1017/9781108349161.011

Ultra-commutative monoids

Schwede, S. (2018) · Stefan Schwede eBooks · doi:10.1017/9781108349161.003

Unramified Milnor–Witt K-Theories

Morel, F. (2012) · Lecture notes in mathematics · doi:10.1007/978-3-642-29514-0_3

Unstable modules with only the top k Steenrod operations

Li, Z. (2021) · Algebraic & Geometric Topology · doi:10.2140/agt.2021.21.3623

Equivariant spaces

Schwede, S. (2018) · doi:10.1017/9781108349161.009

Preface

Schwede, S. (2018) · doi:10.1017/9781108349161.001

Unstable global homotopy theory

Schwede, S. (2018) · Stefan Schwede eBooks · doi:10.1017/9781108349161.002

Ultra-commutative ring spectra

Schwede, S. (2018) · Stefan Schwede eBooks · doi:10.1017/9781108349161.006

Compactly generated spaces

Schwede, S. (2018) · doi:10.1017/9781108349161.008

Hurewicz and Poincare Theorems for Simplicial Modules

ÇAĞLAYAN, E. I. (2022) · Fundamental Journal of Mathematics and Applications · doi:10.33401/fujma.1031108

R-Acyclicit�

Idrissi-Chlihi, M. (1980) · Mathematische Zeitschrift · doi:10.1007/bf01293531

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Index

Schwede, S. (2018) · Stefan Schwede eBooks · doi:10.1017/9781108349161.012

Representations up to coherent homotopy

Porter, T., & Stasheff, J. (2023) · Journal of Geometry and Physics · doi:10.1016/j.geomphys.2023.104966

On classifying simplicial modules

Arvasi, Z., & ÇAĞLAYAN, E. I. (2023) · Communications in Algebra · doi:10.1080/00927872.2023.2255266

Are two H-spaces homotopy equivalent? An algorithmic view point

Šimková, M. (2023) · Journal of Topology and Analysis · doi:10.1142/s1793525323500437

Duals of higher vector spaces

Ronchi, S., & Zhu, C. (2026) · Journal of Geometry and Physics · doi:10.1016/j.geomphys.2026.105971

Simplicial homology

Prasolov, V. (2007) · Graduate studies in mathematics · doi:10.1090/gsm/081/01

Simplicial objects and homotopy theory

Smirnov, V. (2001) · Translations of mathematical monographs · doi:10.1090/mmono/198/02

Examples of simplicial homotopy theories

Quillen, D. G. (1967) · Lecture notes in mathematics · doi:10.1007/bfb0097440 · Cited by 1

Simple-homotopy theory

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Proper homotopy theory in simplicial complexes

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