An embedding theorem for adhesive categories

Adhesive categories are categories which have pushouts with one leg a monomorphism, all pullbacks, and certain exactness conditions relating these pushouts and pullbacks. We give a new proof of the fact that every topos is adhesive. We also prove a converse: every small adhesive category has a fully faithful functor in a topos, with the functor preserving the all the structure. Combining these two results, we see that the exactness conditions in the definition of adhesive category are exactly the relationship between pushouts along monomorphisms and pullbacks which hold in any topos.Comment: 8 page

Sprawling by the Lake: How IDA-Granted Property Tax Exemptions Undermine Older Parts of the Buffalo/Niagara Metro Area

An examination of the geographic distribution of property tax exemptions given to businesses in 2005 by the nine state-regulated Industrial Development Agencies (IDAs) in the Buffalo/Niagara metro area reveals they have subsidized job creation outside of the region’s oldest, most densely populated and most transit-accessible areas, despite the fact those areas are most in need of jobs and reinvestment. The exemptions’ sprawling, pro-suburban bias is especially evident in Erie County and far less problematic in Niagara

Morita contexts as lax functors

Monads are well known to be equivalent to lax functors out of the terminal category. Morita contexts are here shown to be lax functors out of the chaotic category with two objects. This allows various aspects in the theory of Morita contexts to be seen as special cases of general results about lax functors. The account we give of this could serve as an introduction to lax functors for those familiar with the theory of monads. We also prove some very general results along these lines relative to a given 2-comonad, with the classical case of ordinary monad theory amounting to the case of the identity comonad on Cat.Comment: v2 minor changes, added references; to appear in Applied Categorical Structure

Good work, little soldier: Text and pretext

This article reads the relation between Denis's Beau Travail and Jean-Luc Godard's 1960 film Le Petit Soldat as a film-on-film variant of film-on-book adaptation. The model informing this reading is not so much intertextual as pretextual. The principal points of contact between the two films discussed are 'actor' (Michel Subor), 'character' (Bruno Forestier) and 'narrator' (Forestier/Galoup). The use in Beau Travail of Le Petit Soldat is compared with and differentiated from the use of Melville's 'Billy Budd, Sailor'. The conclusion arrived at is that the film-on-film relation can be read as a development of the mirror motif borrowed from Godard by Denis, in order to replace abyssal models of intertextual infinity with the finitudes of abyssal reflexivity. This is to offer a model of pretextuality that is not dependent on privileging the pretext: implicit is the suggestion that Beau Travail and Le Petit Soldat may be read as a single, if hybrid, text

On monads and warpings

We explain the sense in which a warping on a monoidal category is the same as a pseudomonad on the corresponding one-object bicategory, and we describe extensions of this to the setting of skew monoidal categories: these are a generalization of monoidal categories in which the associativity and unit maps are not required to be invertible. Our analysis leads us to describe a normalization process for skew monoidal categories, which produces a universal skew monoidal category for which the right unit map is invertible.Comment: 15 pages. Version 2: revised based on a very helpful report from the referee. To appear in the Cahiers de Topologie and Geometrie Differentielle Categorique

Free skew monoidal categories

In the paper "Triangulations, orientals, and skew monoidal categories", the free monoidal category Fsk on a single generating object was described. We sharpen this by giving a completely explicit description of Fsk, and so of the free skew monoidal category on any category. As an application we describe adjunctions between the operad for skew monoidal categories and various simpler operads. For a particular such operad L, we identify skew monoidal categories with certain colax L-algebras.Comment: v2: changed title, otherwise minimal change

On the axioms for adhesive and quasiadhesive categories

A category is adhesive if it has all pullbacks, all pushouts along monomorphisms, and all exactness conditions between pullbacks and pushouts along monomorphisms which hold in a topos. This condition can be modified by considering only pushouts along regular monomorphisms, or by asking only for the exactness conditions which hold in a quasitopos. We prove four characterization theorems dealing with adhesive categories and their variants.Comment: 20 pages; v2 final version, contains more details in some proof