Australian Category Seminar

Objective Mackey and Tambara functors (abs)

Wood fusion for closed comonads (abs)

Wood fusion for magmal comonads (abs)

Report on the book: "Mackey 2-Functors and Mackey 2-Motives" by Balmer and Dell'Ambrogio (abs)

Monoidal centres and groupoid-graded categories (abs)

Thoughts on the paper “Generic representation theory of finite fields in nondescribing characteristic” by N.J. Kuhn (abs)

The groupoid core can suffice (abs)

Variations on a comprehensive theme (abs)

Two sides to every storey (abs)

Examples of abstracted polynomials, and Kleisli bicategories (abs)

The nucleus of an adjunction (abs)

The monoidal centre for group-graded categories (abs)

More on fake pullbacks (abs)

Polynomic thoughts (abs)

⤳ from 13 Feburary

Polynomic rethink (abs)

Spans, Relations, and all that (abs)

The free dual pair (abs)

Polynomials of various hues (abs)

The Burau representation extended to tangles (abs)

Reminiscing on [5] (abs)

Parcels (joint with Branko Nikolic) (abs)

The scarcity of vector product algebras (abs)

Composition algebras (abs)

Local convolution and $\mathbf{MonCat}$-bicategories

Toil and trouble with Drinfeld's double

Real sets (abs)

Series monoidal categories and Zeno functors (abs)

Quadratic forms as complete invariants for autonomous braided monoidal groupoids (abs)

Cauchy completeness for DG-categories (abs)

⤳ from 5 July (abs)

Raising Cauchy through a comonadic base change (abs)

Wreath convolution

Mixed wreaths

Monoidal twisted coactions

Reminder on Kock-Zoberlein monads

A factorization for closed functors

Weighted convolution of Joyal species, and related concepts

⤳ from 4 Feburary

A skew view of lax algebras

The free mixed distributive law

Tambara's work on finite categories

⤳ from 15 July

The twisted arrow category

A setting for some equivalences of additive presheaf categories

Even more on combinatorial categorical equivalences

Comparison of adjunctions between free cocompletions

Skew reflections

Semiadjoints

A monoidal miscellany

Flocks askew

Convolution

Pointwise extensions in bicategories

Limit sketches in bicategories

The Davydov-Runkel BMC alternative (abs)

An equivalence of categories relevant to combinatorics and representation theory (abs)

Morita equivalence of strong epimorphisms and partial maps

Relations

Pointwise left extensions inside 2-categories (abs)

More on internal full subcategories (abs)

Quantum categories following Kornel Szlachanyi (arXiv:1201.4981v1) (abs)

⤳ from 21 March

Skew-promonoidal categories (abs)

Skew-monoidal 2-functors

On Appendix 2 of Brian Day's PhD Thesis (abs)

Oriented simplexes and the Tamari lattice

Another tilt at free skew-monoidal categories

Monoidal monoidal thoughts

Remarks on the work of Davydov

Charades

Aspects of duoidal categories

Remarks on cartesian morphisms

Well-formed words

Back to normality

Hopf bimonoids in duoidal categories

Categories in categories (abs)

⤳ from 7 December

⤳ from 14 December

Drinfeld's approach to geometric realization (abs)

Recollections on DG-categories

Enrichment of Hirata's Morita theory (with Tom Booker) (abs)

Simple Roots Of Separability

Separable enriched categories and their modules

Trace à la arXiv:1010.4527v1

Weak distributive laws

Some observations about monads such as doctrinal adjunction, Hopf monads, and weak distributive laws

Powerful morphisms, comprehensive factorization, and torsors

⤳ from 6 May

Elementary results on torsors

Remarks on the Day reflection theorem

Flocks: some more on torsors

Quantum presheaves

⤳ from 2 April

Lax adjunction

Double categories for better or worse

Separable functors, Yang-Baxter operators, and bimonoids

Bimonoidal and separable monoidal functors

Bicategories of modules

Filtered colimits and other concepts

Another category of G-sets

Doubles for monoidal categories

Comonads and *-autonomy

Hom lifting

More work based on Tambara's

Fine tuning on last week's talk

Localizations; centres and doubles

*-Autonomy for the category of Mackey functors

Autonomous categories, autonomous bicategories, and quantum modules

Some remarks on 'When Hopf algebras are Frobenius algebras', a paper of Bodo Pareigis

Weak bimonoids in braided monoidal categories

Kan extensions in basic group representation theory

Promonoidal braiding and centre

⤳ from 5 January

Lax braidings and lax centres

Frobenius algebras and quantum groupoids

Higher adjoint equivalences

Convolution-enriched categories and centre

Comodules and coproduct decomposition (abs)

What is the Cauchy completion of a monoidal functor?

Centres of localization

Frobenius algebras and pseudo-algebras (abs)

Frobenius equals star-autonomous (abs)

Convolution and actegories

G-sets and V-actegories as enriched categories

Cauchy completion, centres, and Frobenius algebras

String diagrams for monoidal categories

Monoids and things monoidal

Elementary category theory

Functors between categories of G-sets

Application of the special adjoint functor theorem

The lax centre for cartesian presheaf categories

⤳ from 27 November 2002

Categorical and combinatorial aspects of descent theory (abs)

⤳ from 5 March

Weak orientals and the simplicial nerve of a weak n-category

The monoidal centre as a limit (abs)

Filtered, percolated or espresso?

A more explicit description of quantum groupoids

⤳ from 20 August

Update on the efficient construction of real numbers

Objective numbers

Categorically less radical radicals

Remarks on the simplicial categories

Roots of unity as a Lie algebra II

Modules for substitudes (abs)

A collage of odds and coends related to operads

A factorization system inter alia pertaining to descent (abs)

A need for descent in variable bicategories

Even more braidings (abs)

Quantum groupoids, modules and star-autonomy (abs)

⤳ from 20 November

Extraordinary stuff for the antipodes (abs)

New PROPS and 2-PROPS

Autonomous monoidal functors and their categorification

More on autonomous pseudomonoids

Lax monoids and convolutions

Weak ω-categories (abs)

L' (abs)

More on lax monoids (abs)

Roots of unity as a Lie algebra (abs)

Monads and extended distributive laws (abs)

Multicategories and operads in Cat-operads (abs)

Duality for finite groups

Batanin-Joyal higher categories without trees (Deforestation for a global village)

Berger's homogeneous theory structure on Joyal's category Θ

On the cellular nerves of ω-categories

Yang-Baxter operators on monoids

Cohomology of groups

Categories enriched on two sides

The formal theory of monads revisited

Oh no! Not even weaker 3-categories!

Cohomology with coefficients in a category

From modules to accessible functors

An extension of Grothendieck's semidirect/wreath product construction arising from enriched category theory (abs)

A braiding for Pointed Groups (abs)

Operads without numbers (abs)

Analytic functors on globular sets

Internal categories (abs)

The naturality of twist (abs)

The chain rule

Morita Rivista (abs)

Long modules, half-Long modules, and the Knizhnik-Zamolodchikov equation

Holiday thoughts on Tannaka duality (abs)

The Charade Braid

The higher operads of Michael Batanin (abs)

Zen from three conferences (abs)

Finite coproducts in variable categories (abs)

Parenthetic remarks (abs)

Footnote to parenthetic remarks

More on the Quantum Double (abs)

Coming to terms with opcategories (abs)

⤳ from 21 August

The Chu Construction (abs)

Fusion operators as generalised Hopf structures (abs)

Transfer of limits across functors (abs)

Group Cohomology

Some parametrized categorical concepts I (abs)

A Letter From Max To Ross, McGill 15/3/86 (abs)

Some Parametrized Categorical Concepts II (abs)

Some Parametrized Concepts III (abs)

Braided monoidal categories (abs)

Why there are no loops (abs)

Some remarks on group cohomology (abs)

Paré on tripleability of Compact Hausdorff Spaces