Compositories and Gleaves
نویسندگان
چکیده
Sheaves are objects of a local nature: a global section is determined by how it looks locally. Hence, a sheaf cannot describe mathematical structures which contain global or nonlocal geometric information. To fill this gap, we introduce the theory of “gleaves”, which are presheaves equipped with an additional “gluing operation” of compatible pairs of local sections. This generalizes the conditional product structures of Dawid and Studený, which correspond to gleaves on distributive lattices. Our examples include the gleaf of metric spaces and the gleaf of joint probability distributions. A result of Johnstone shows that a category of gleaves can have a subobject classifier despite not being cartesian closed. Gleaves over the simplex category ∆, which we call compositories, can be interpreted as a new kind of higher category in which the composition of an m-morphism and an n-morphism along a common k-morphism face results in an (m + n − k)-morphism. The distinctive feature of this composition operation is that the original morphisms can be recovered from the composite morphism as initial and final faces. Examples of compositories include nerves of categories and compositories of higher spans.
منابع مشابه
Probabilistic analysis of transport-reaction processes over catalytic particles: theory and experimental testing
We develop a probabilistic theory for conversion of A→ B processes for a model Temporal Analysis of Products (TAP)-like experiments based on the general theory of Brownian motion with killing and the Feynman-Kac formula. Initial experimental testing for systems with a single catalyst particle is given, as well as numerical experiments for two-particle catalyst systems in simple geometric config...
متن کاملFalse and Recovered Memories in the Laboratory and Clinic : A Review of Experimental and Clinical Evidence
Blocked and recovered memories of traumatic events have long been regarded as real phenomena by the mental health profession, our legal system, and the public at large. These phenomena originally were studied by Pierre Janet and Sigmund Freud, and Freud’s (1896/1962) ‘‘Aetiology of Hysteria’’ is perhaps the best known early discussion of this topic. In this now famous 1896 address, Freud presen...
متن کاملEndothelial Hif Signaling Regulates Pulmonary Fibrosis-
ASSOCIATED PULMONARY HYPERTENSION 2 3 Andrew J. Bryant, M.D., Ryan P. Carrick, M.D., Melinda E. McConaha, M.S., 4 Brittany R. Jones, B.S., Sheila D. Shay, B.S., Christy S. Moore, B.S., Thomas R. 5 Blackwell, B.S., Santhi Gladson, M.S., Niki L. Penner, Ankita Burman, M.S., 6 Harikrishna Tanjore, Ph.D., Anna R. Hemnes, M.D., Ayub K. Karwandyar, B.S., 7 Vasiliy V. Polosukhin, M.D., Ph.D., Sc.D., M...
متن کاملLyme disease in Oregon.
The incidence of Lyme disease in Oregon is calculated from cases reported to the Oregon State Health Division. We reviewed the exposure history of reported cases of Lyme disease and performed field surveys for infected Ixodes pacificus ticks. The incidence of Lyme disease correlated with the distribution of infected I. pacificus ticks.
متن کامل