Australian Category Seminar

The free monoidal differential modality (abs)

What I did on my holidays

Powerset and Vietoris, universally (abs)

Isotropy Groups (abs)

Perspectives on V (abs)

Centralisers, centres and all that (abs)

Some recherche monoidal structures (abs)

Volterra series (abs)

Bisimulation versus trace equivalence (abs)

Varieties of [B|M]-sets (abs)

⤳ from 8 June

The topological behaviour category of an algebraic theory (abs)

A view on codifferential categories (abs)

Tensor products of models and comodels in computer science (abs)

Continuous functions on streams (abs)

Probabilistic automata as comodels in models (abs)

The dependently typed update monad (abs)

Completeness for comodels (abs)

Categories of comodels (abs)

Cartesian closed varieties (abs)

⤳ from 30 September (abs)

⤳ from 14 October (abs)

J–T, V, L and F (abs)

Inner automorphisms of groupoids (abs)

Cartesian differential categories as skew-enriched categories (abs)

Topos theoretic aspects of self-similarity (abs)

Fixpoint toposes (abs)

The free tangent category on an object with affine connection (abs)

Parametric right adjoint functors and polynomials (abs)

Relative extensivity, multicategories and topological spaces (abs)

Comonads and enrichment (abs)

Institutions

The Giry tricocycloid (abs)

Operadic categories and decalage (abs)

The locally connected classifying topos (abs)

Polynomial monads as fibred PROPs (abs)

The Vietoris monad via weak distributive laws (abs)

Hypernormalisation and linear exponential monads (abs)

The disintegration operadic category (abs)

Unary operadic categories and discrete decomposition spaces (abs)

Chu spaces and the funny tensor product (abs)

A practical introduction to weighted limits (abs)

Ultraproducts, ultraspans and ultracategories (abs)

Monads and theories (abs)

A new and improved embedding theorem for tangent categories (abs)

(Co)localisation of one-dimensional model structures (abs)

The model bicategory of model categories

Ultrafilters, restriction categories and "Maschke's lemma"

Monads extending from Set to Rel

Right properness of simplicial sets a la arXiv:1510.00669

Mixed opwreaths and coherence spaces

Non-standard arities

Generalised Lawvere theories via enrichment

In search of a terminal biring

An efficient construction of the orientals

How not to enrich over a duoidal category

Remarks on crossed internal categories in toposes

When coproducts are biproducts

The Campbell–Baker–Hausdorff adjunction

Synthetic differentiation of species

An embedding theorem for tangent categories

Shapely monads and analytic functors on presheaf categories

⤳ from 29 July

⤳ from 5 August

⤳ from 12 August

Toric varieties and manifolds a la Grandis–Cockett

Remarks on Catalan sets

Ordinal notation

More ordinal notation

Reedy categories, Grothendieck fibrations, and the Isbell envelope

The Isbell monad

Re-revisiting the nerve theorem

The formal theory of monads 1.5

The uniform family approach to realizability toposes

Fibred lex colimits

⤳ from 8 October

Quasicategorical lalis, with applications to quasicategorical limits and colimits, Grothendieck fibrations, Kan extensions, and so on

Homological lalis

⤳ from 3 December

Dendroidal resolution of dg-operads

Cofibrant simplicial sets

More on cofibrant simplicial sets

Finitary monads, Lawvere theories, and Cauchy completion

⤳ from 1 May

Expository remarks on fat orthogonal reflection

Topological = total

⤳ from 19 June

Expository remarks on Dedekind–Mac Neille–Isbell–Lambek completion

Combinatorial structure of type dependency

⤳ from 2 October

⤳ from 16 October

Universal properties of Poly(E)

⤳ from 30 October

Reedy remarks

Une catéade, qu'est-ce que c'est? (abs)

⤳ from 18 January

Regular 2-categories (abs)

⤳ from 21 March

⤳ from 28 March

The so-exact completion of a 2-category (abs)

The fformal theory of monads (abs)

Monads that extend from Set to Rel

T-multicategories and their morphisms, for T a 2-monad on Cat which extends to Prof, characterised, under mild side conditions, as the Eilenberg-Moore category for the lax morphism classifier comonad on T-Alg_s

⤳ from 10 October

⤳ from 17 October

⤳ from 24 October

Remarks on comprehensive factorisation

⤳ from 5 December

Lex colimits

⤳ from 16 Feburary

Stone Duality

What I did on my holidays

Introduction to type theory

⤳ from 6 April

⤳ from 13 April

The Schanuel topos

1001 characterisations of pie

On "On the essentially algebraic theory generated by a sketch"

Restriction categories as enriched categories

Categories in which effective descent = regular epimorphism

A somewhat malleable proof that finite limits commute with filtered colimits

A characterisation of algebraic exactness

Three flavours of pie

Yes, you, too, could have invented plethysm

Weighted limits

Pushouts characteristic of the pretopos

More Mal'cev musings

⤳ from 14 December

Something for everyone

Simplicial Homotopies

Extremely elementary group cohomology

Commutativity

Abstractly analysing analyticity

⤳ from 15 September

Revisiting the nerve theorem

⤳ from 6 October

Type theory, weak ω-categories, and all that

Ionads: a generalisation of the notion of topological space

⤳ from 28 October

Weak maps

Presentations of factorisation systems