The Realistic Angel: Pictorial Realism as Hypothetical Verity

My main objective in this paper is to formulate a view of pictorial realism I call ‘hypothetical verity’. It owes much to John Kulvicki but diverges from his view in an important respect: rather than thinking that realistic pictures are true to our conceptions of things, I hold that they are true to what things would be like if they existed. In addition, I agree with Dominic Lopes that different realisms reflect different aspects of reality, but restate the case without recourse to symbol systems. Together, the twin principles of hypothetical verity and aspectival absolutism constitute a theory of realism able to account for realistic fictional entities, the problem of revelatory realism and images that teach new information

Kan extensions and the calculus of modules for ∞\infty-categories

Various models of $(\infty,1)$-categories, including quasi-categories, complete Segal spaces, Segal categories, and naturally marked simplicial sets can be considered as the objects of an $\infty$-cosmos. In a generic $\infty$-cosmos, whose objects we call $\infty$-categories, we introduce modules (also called profunctors or correspondences) between $\infty$-categories, incarnated as as spans of suitably-defined fibrations with groupoidal fibers. As the name suggests, a module from $A$ to $B$ is an $\infty$-category equipped with a left action of $A$ and a right action of $B$, in a suitable sense. Applying the fibrational form of the Yoneda lemma, we develop a general calculus of modules, proving that they naturally assemble into a multicategory-like structure called a virtual equipment, which is known to be a robust setting in which to develop formal category theory. Using the calculus of modules, it is straightforward to define and study pointwise Kan extensions, which we relate, in the case of cartesian closed $\infty$-cosmoi, to limits and colimits of diagrams valued in an $\infty$-category, as introduced in previous work.Comment: 84 pages; a sequel to arXiv:1506.05500; v2. new results added, axiom circularity removed; v3. final journal version to appear in Alg. Geom. To

Completeness results for quasi-categories of algebras, homotopy limits, and related general constructions

Consider a diagram of quasi-categories that admit and functors that preserve limits or colimits of a fixed shape. We show that any weighted limit whose weight is a projective cofibrant simplicial functor is again a quasi-category admitting these (co)limits and that they are preserved by the functors in the limit cone. In particular, the Bousfield-Kan homotopy limit of a diagram of quasi-categories admit any limits or colimits existing in and preserved by the functors in that diagram. In previous work, we demonstrated that the quasi-category of algebras for a homotopy coherent monad could be described as a weighted limit with projective cofibrant weight, so these results immediately provide us with important (co)completeness results for quasi-categories of algebras. These generalise most of the classical categorical results, except for a well known theorem which shows that limits lift to the category of algebras for any monad, regardless of whether its functor part preserves those limits. The second half of this paper establishes this more general result in the quasi-categorical setting: showing that the monadic forgetful functor of the quasi-category of algebras for a homotopy coherent monad creates all limits that exist in the base quasi-category, without further assumption on the monad. This proof relies upon a more delicate and explicit analysis of the particular weight used to define quasi-categories of algebras.Comment: 33 pages; a sequel to arXiv:1306.5144 and arXiv:1310.8279; v3: final journal version with updated internal references to the new version of "Homotopy coherent adjunctions and the formal theory of monads

Designació dels lectotipus de Pseudochazara williamsi (Romei, 1927) (Lepidoptera: Nymphalidae: Satyrinae) i Carcharodus tripolinus (Verity, 1925) (Lepidoptera: Hesperiidae: Pyrginae) de la col·lecció d'Ignasi de Sagarra dipositada al Museu de Ciències Naturals de Barcelona

Es designa el lectotipus de Pseudochazara williamsi (Romei, 1927) procedent de la localitat típica de Puerto del Lobo, Sierra Nevada, Granada, Andalusia, Espanya i el de Carcharodus tripolinus (Verity, 1925) procedent de la localitat típica de Garian plateau, Trípoli, Líbia.The lectotype of Pseudochazara williamsi (Romei, 1927) is designated, from its typical locality of Puerto del Lobo, Sierra Nevada, Granada, Andalucia, Spain. The lectotype of Carcharodus tripolunus (Verity, 1925) is designated, from its typical locality of Garian plateau, Tripoli, Libya

Quantum Turing automata

A denotational semantics of quantum Turing machines having a quantum control is defined in the dagger compact closed category of finite dimensional Hilbert spaces. Using the Moore-Penrose generalized inverse, a new additive trace is introduced on the restriction of this category to isometries, which trace is carried over to directed quantum Turing machines as monoidal automata. The Joyal-Street-Verity Int construction is then used to extend this structure to a reversible bidirectional one.Comment: In Proceedings DCM 2012, arXiv:1403.757