FungusA fungus (: fungi or funguses) is any member of the group of eukaryotic organisms that includes microorganisms such as yeasts and molds, as well as the more familiar mushrooms. These organisms are classified as a kingdom, separately from the other eukaryotic kingdoms, which, by one traditional classification, includes Plantae, Animalia, Protozoa, and Chromista. A characteristic that places fungi in a different kingdom from plants, bacteria, and some protists is chitin in their cell walls.
Spectral sequenceIn homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization of exact sequences, and since their introduction by , they have become important computational tools, particularly in algebraic topology, algebraic geometry and homological algebra. Motivated by problems in algebraic topology, Jean Leray introduced the notion of a sheaf and found himself faced with the problem of computing sheaf cohomology.
Wood-decay fungusA wood-decay or xylophagous fungus is any species of fungus that digests moist wood, causing it to rot. Some species of wood-decay fungi attack dead wood, such as brown rot, and some, such as Armillaria (honey fungus), are parasitic and colonize living trees. Excessive moisture above the fibre saturation point in wood is required for fungal colonization and proliferation. In nature, this process causes the breakdown of complex molecules and leads to the return of nutrients to the soil.
Derived functorIn mathematics, certain functors may be derived to obtain other functors closely related to the original ones. This operation, while fairly abstract, unifies a number of constructions throughout mathematics. It was noted in various quite different settings that a short exact sequence often gives rise to a "long exact sequence". The concept of derived functors explains and clarifies many of these observations. Suppose we are given a covariant left exact functor F : A → B between two A and B.
ProtistA protist (ˈproʊtᵻst ) or protoctist is any eukaryotic organism that is not an animal, plant, or fungus. Protists do not form a natural group, or clade, but an artificial grouping of several independent clades that evolved from the last eukaryotic common ancestor. Protists were historically regarded as a separate taxonomic kingdom known as Protista or Protoctista. With the advent of phylogenetic analysis and electron microscopy studies, the use of Protista as a formal taxon was gradually abandoned.
EukaryoteThe eukaryotes constitute the domain of Eukaryota (juːˈkærioʊts,_-əts), organisms whose cells have a nucleus. All animals, plants, fungi, and many unicellular organisms are eukaryotes. They constitute a major group of life forms, alongside the two groups of prokaryotes, the Bacteria and the Archaea. Eukaryotes represent a small minority of the number of organisms, but due to their generally much larger size, their collective global biomass is much larger than that of prokaryotes.
Derived categoryIn mathematics, the derived category D(A) of an A is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on A. The construction proceeds on the basis that the of D(A) should be chain complexes in A, with two such chain complexes considered isomorphic when there is a chain map that induces an isomorphism on the level of homology of the chain complexes. Derived functors can then be defined for chain complexes, refining the concept of hypercohomology.
Exact sequenceAn exact sequence is a sequence of morphisms between objects (for example, groups, rings, modules, and, more generally, objects of an ) such that the of one morphism equals the kernel of the next. In the context of group theory, a sequence of groups and group homomorphisms is said to be exact at if . The sequence is called exact if it is exact at each for all , i.e., if the image of each homomorphism is equal to the kernel of the next. The sequence of groups and homomorphisms may be either finite or infinite.
TruffleA truffle is the fruiting body of a subterranean ascomycete fungus, predominantly one of the many species of the genus Tuber. In addition to Tuber, over one hundred other genera of fungi are classified as truffles including Geopora, Peziza, Choiromyces, and Leucangium. These genera belong to the class Pezizomycetes and the Pezizales order. Several truffle-like basidiomycetes are excluded from Pezizales, including Rhizopogon and Glomus. Truffles are ectomycorrhizal fungi, so they are usually found in close association with tree roots.
AscomycotaAscomycota is a phylum of the kingdom Fungi that, together with the Basidiomycota, forms the subkingdom Dikarya. Its members are commonly known as the sac fungi or ascomycetes. It is the largest phylum of Fungi, with over 64,000 species. The defining feature of this fungal group is the "ascus" (), a microscopic sexual structure in which nonmotile spores, called ascospores, are formed. However, some species of the Ascomycota are asexual, meaning that they do not have a sexual cycle and thus do not form asci or ascospores.
