nLab list of theses in category theory

This page is intended to record doctoral theses whose focus is primarily category theoretic, particularly those from earlier years that are harder to find online.

Note: the list is ordered first by year, then alphabetically by last name.

Title	Author	Year	URL	Summary
Exact Categories and Duality	David Buchsbaum	1954	doi	on homological algebra in abelian categories
Representations for Dicategories	Stanley Parlett Hughart	1954	doi	on factorisation systems
Functor theory	Peter Freyd	1960	Category Theory Archive
Des Catégories Abéliennes	Pierre Gabriel	1960	numdam	on abelian categories
Functorial Semantics of Algebraic Theories	William Lawvere	1963	TAC reprint	on algebraic theories
The Functorial Foundations of Measure Theory	Fred Linton	1963	Scan	on measure theory
Categories of Set Valued Functors	Marta Bunge	1966	ProQuest	on categories of presheaves
Fibred Categories and the Theory of Structures (Part I)	John Duskin	1966	McMaster repository
Triples, algebras and cohomology	Jon Beck	1967	TAC reprint
A triple miscellany: some aspects of the theory of algebras over a triple	Ernest Manes	1967	proquest
Limit monads in categories	Anders Kock	1967	proquest	on lax idempotent 2-monads
Homotopy Classification of Filtered Complexes	Ross Street	1968	Scan
Absoluteness properties in category theory	Robert Paré	1969	Scan	on absolute colimits
Construction of Biclosed Categories	Brian Day	1970	Scan
A categorical approach to universal algebra	Bob Walters	1970	ANU repository	on universal algebra
Self-Dual Structure-Semantics and Algebraic Categories	Michel Thiébaud	1971
Tensor and cotensor products of bifunctors	George D. Reynolds	1973
Some Aspects of Internal Category Theory in an Elementary Topos	Peter Johnstone	1974
Relative Bildzerlegungen und algebraische Kategorien	Walter Tholen	1974	Scan	English translation of the title is Relative image decompositions and algebraic categories
Coherence for a closed functor	Geoffrey Lewis	1974	UNSW repository
Catégories internes et fibrations ; Cohomologie de Gel’fand-Fuks	Jean Celeyrette	1975	Jean Celeyrette's 1975 thesis	internal categories, fibrations, Gelfand-Fuks cohomology
Théorie formelle des bicatégories	Syméon Bozapalides	1976	Scan	on 2-dimensional coends, enriched bicategories, etc.
Universal coalgebras	Thomas Fox	1976	McGill repository
Indicial methods for relative categories	Richard Wood	1976	Dalhousie repository
Some existence theorems in the theory of doctrines	Robert Blackwell	1976	UNSW repository
Abstract Families of Algebras	Robert Rosebrugh	1977
Catégories localisables & Aspects geometriques de la propriete de Radon-Nikodym dans les espaces de Banach	Yves Diers	1977	Category Theory Archive	on locally multipresentable categories, among other things
Cartesianess	Susan Niefield	1978	proquest	on exponentiable objects (there called “cartesian objects”)
Algebraic and locally algebraic functors	James J. Dukarm	1980	Scan	on locally equational categories
The Theory of Triposes	Andrew Pitts	1981	Scan	on triposes
Limits in 2-categories of locally presentable categories	Greg Bird	1984	Scan	on flexible limits, lax morphism classifiers, and locally presentable categories
Operational Categories	Colin Barry Jay	1984	Category Theory Archive
Butler’s theorems and adjoint squares	John Power	1984	Scan	on the adjoint lifting theorem and adjoint triangle theorem
Pasting diagrams in n-categories with applications to coherence theorems and categories of paths	Michael Johnson	1988	postscript
Predicates and Fibrations	Duško Pavlović	1990	Scan
Dialectica Categories	Valeria de Paiva	1991	Computer Lab Technical Report
Enriched categories, internal categories and change of base	Dominic Verity	1992	TAC reprint
Cauchy completion in enriched categories	Scott Russell Johnson	1993	ANU repository
Linear Logic, Bimodules, and Full Coherence for Autonomous Categories	Todd Trimble	1994
Cobordism Categories	Sean Carmody	1995
The algebra of distributive and extensive categories	Stephen Lack	1995
Ultraproducts and continuous families of models	Francisco Marmolejo	1995	pdf	on ultracategories, treated 2-monadically
Groupoid Representations for Sheaves on Orbifolds	Dorette Pronk	1995
Internal categories and quantum groups	Marcelo Aguiar	1997	pdf
Full Completeness for models of Linear Logic	Audrey Tan?	1997	pdf
Monadicity, Purity, and Descent Equivalence	Xiuzhan Guo	2000	pdf	on monadicity, descent, and locally presentable categories
Higher-Dimensional Category Theory: Opetopic Foundations	Eugenia Cheng	2002	pdf
Polycategories	Richard Garner	2006	PDF	on polycategories via Kleisli bicategories and mixed distributive laws
An algebraic theory of tricategories	Nick Gurski	2007	pdf
Bigroupoid 2-torsors	Igor Baković	2008	doi	on principal 2-bundles
Coherence for Categorified Operadic Theories	Miles Gould	2008	Glasgow repository	on categorification, coherence and operads
Double Categories and Base Change in Homotopy Theory	Michael Shulman	2009	ProQuest
Codescent objects in 2-dimensional universal algebra	John Bourke	2010	pdf	on codescent objects and 2-dimensional generalisations of internal categories
Homology operations in the spectral sequence of a cosimplicial space	Philip Hackney	2010	pdf
On constructions of left determined model structures	Marc Olschok	2010	pdf
On categories of algebras	Jan Pavlík	2010	pdf
Fundamental bigroupoids and 2-covering spaces	David Michael Roberts	2010	Adelaide repository
Algebraic Model Structures	Emily Riehl	2011	pdf
Algebraic weighted colimits	Seerp Roald Koudenburg	2014	arXiv	On left extensions and weighted colimits for algebras for monads on double categories
Grothendieck categories of enriched functors	Hassan Al Hwaeer	2014	core
Analysis and construction of logical systems: a category-theoretic approach	Michał R. Przybyłek	2014	pdf
Generalization of Algebraic Operations via Enrichment	Christina Vasilakopoulou	2014	arXiv
Three studies in higher category theory: fibrations, skew monoidal structures and excision of extremals	Mitchell Buckley	2015	Macquarie repository
Synthetic Lie theory	Matthew Burke	2015	Macquarie repository
Fibrations of predicates and bicategories of relations	Finn Lawler	2015	arXiv
Sketches in higher category theory	Remy Vincent Tuyeras	2015	Macquarie repository
A higher categorical approach to Giraud’s non-abelian cohomology	Alexander Campbell	2016	Macquarie repository
The Algebra of Open and Interconnected Systems	Brendan Fong	2016	arXiv
Oplax actions and enriched icons with applications to coalgebroids and quantum categories	Ramón Abud Alcalá	2017	Macquarie repository
Tangent bundles, monoidal theories, and Weil algebras	Poon Leung	2017	Macquarie repository
The Way of the Dagger	Martti Karvonen	2018	arXiv
Morphisms of 2-dimensional structures with applications	Branko Nikolić	2018	Macquarie repository
Categorical probability and stochastic dominance in metric spaces	Paolo Perrone	2018	pdf	on categorical probability theory
Compact symmetric multicategories and the problem of loops	Sophie Raynor	2018	Aberdeen repository
Homotopy theory of Grothendieck ∞-groupoids and ∞-categories	Edoardo Lanari	2019	Macquarie repository
Restriction presheaves and restriction colimits	Daniel Lin	2019	Macquarie repository
Structures in two dimensional category theory and applications to polynomial functors	Charles Walker	2019	Macquarie repository
The Scott adjunction	Ivan Di Liberti	2020	arXiv
Cartesian closed bicategories: type theory and coherence	Philip Saville	2020	arXiv
The Gray tensor product for 2-quasi-categories	Yuki Maehara	2020	Macquarie repository
Toposes of Monoid Actions	Morgan Rogers	2021	arXiv
Monadic and Higher-Order Structure	Nathanael Arkor	2022	Cambridge repository	on relative monads, second-order algebraic theories, and monad–theory correspondences in a proarrow equipment
Pseudomonads, Relative Monads and Strongly Finitary Notions of Multicategory	Gabriele Lobbia	2022	Leeds repository
Large cardinals and $\infty$-categories	Giulio Lo Monaco	2022	Masaryk repository
Topics in the theory of enriched accessible categories	Giacomo Tendas	2022	Macquarie repository
Operads in 2-categories and models of structure interchange	Sophie D. Espalungue d’Arros	2023	theses.fr repository
Introspective Theories and Geminal Categories	Sridhar Ramesh	2023	eScholarship repository	on Löb's theorem and the Gödel incompleteness theorem
Scalar Enrichment and Cotraces in Bicategories	Callum William Reader	2023	White Rose repository	on traces and cotraces? in monoidal bicategories
On Monadic Vector-Valued Integration	Benedikt Peterseim	2023	arXiv	on probability monads on convenient categories of topological spaces
Commutativity of Relative Pseudomonads	Andrew Slattery	2024	White Rose repository	on commutative monads, lax-idempotent pseudomonads, and relative pseudomonads
Doctrinal and Groupoidal Representations of Classifying Topoi	Joshua L. Wrigley	2024	PDF

Related pages

• list of journals publishing category theory
• list of theses in category theory
• list of lost manuscripts in category theory
• list of category theory papers that never appeared
• list of textbooks on category theory