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Mathematical concept
model category M, a fibrant object A of M is an object that has a fibration to the terminal object of the category. The fibrant objects of a closed model
Fibrant_object
Abstract homotopical model for topological spaces
model for topological spaces. One model uses Kan complexes which are fibrant objects in the category of simplicial sets (with the standard model structure)
∞-groupoid
Map between simplicial sets with lifting property
and are therefore of fundamental importance. Kan complexes are the fibrant objects in this model category. The name is in honor of Daniel Kan. For various
Kan_fibration
two objects X and Y over an object S is denoted by X × S Y {\displaystyle X\times _{S}Y} and is also called a Cartesian square. fibrant An object is fibrant
Glossary_of_category_theory
Generalization of category theory
the Joyal model structure on the category of simplicial sets, whose fibrant objects are exactly quasi-categories. Recently, in 2009, the theory has been
Higher_category_theory
Mathematician, prolific contributor to homotopy theory
is known as Kan–Quillen model structure, while its fibrations and fibrant objects are known as Kan fibrations and Kan complexes respectively. Some of
Daniel_Kan
Model structure on the category of simplicial sets
equivalences, which fulfill the properties of a model structure. Its fibrant objects are all ∞-categories and it furthermore models the homotopy theory
Joyal_model_structure
f^{*}} is bijective on simplicial homotopy classes for each Kan complex (fibrant object), A fibration is trivial (i.e., has the right lifting property with
Fibration_of_simplicial_sets
Special kind of adjunction between categories named after Daniel Quillen
(right) Quillen functor preserves weak equivalences between cofibrant (fibrant) objects. The total derived functor theorem of Quillen says that the total left
Quillen_adjunction
Mathematical concept in homotopy theory
lemma gives a sufficient condition for a functor on a category of fibrant objects to preserve weak equivalences; the sufficient condition is that acyclic
Ken_Brown's_lemma
Category theory generalization of fumction factorization
{\displaystyle C\cap W.} An object X {\displaystyle X} is called fibrant if the morphism X → 1 {\displaystyle X\rightarrow 1} to the terminal object is a fibration
Factorization_system
Covariant fibrant objects are the left fibrant objects over A {\displaystyle A} . Covariant fibrations between two such left fibrant objects over A {\displaystyle
Co- and contravariant model structure
Co-_and_contravariant_model_structure
Endofunctor on the category of simplicial sets
{\displaystyle \operatorname {Ex} ^{\infty }(X)} is a Kan complex, hence a fibrant object of the Kan–Quillen model structure. This follows directly from the preceding
Extension_(simplicial_set)
Special kind of model structure
model category, in which all objects are cofibrant, is left proper. A model category, in which all objects are fibrant, is right proper. For a model
Proper_model_structure
Homological construction in category theory
the subcategory of “good” (fibrant or cofibrant) objects. By first taking a fibrant or cofibrant resolution of an object and then applying that functor
Derived_functor
Model structure on the category of simplicial sets
equivalences, which fulfill the properties of a model structure. Its fibrant objects are all Kan complexes and it furthermore models the homotopy theory
Kan–Quillen_model_structure
Mathematical category with weak equivalences, fibrations and cofibrations
is fibrant and there is a weak equivalence from X to Z then Z is said to be a fibrant replacement for X. In general, not all objects are fibrant or cofibrant
Model_category
_{*}F\to \pi _{*}G} is an isomorphism. A sheaf of spectra is then a fibrant/cofibrant object in that category. The notion is used to define, for example, a
Sheaf_of_spectra
History of maths
influential paper that defines Browns categories of fibrant objects and dually Brown categories of cofibrant objects 1974 Shiing-Shen Chern–James Simons Chern–Simons
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
Type theory in logic and mathematics
been developed which partition their types into fibrant types, which respect paths, and non-fibrant types, which do not. Cartesian cubical computational
Homotopy_type_theory
equivalence (of simplicial sets) for any C-local object W. An object W is called C-local if it is fibrant (in M) and s ∗ : map ( B , W ) → map ( A ,
Bousfield_localization
Cohomology class
symmetric spectra have quite different behaviour: in S-modules every object is fibrant (which is not true in symmetric spectra), while in symmetric spectra
Highly structured ring spectrum
Highly_structured_ring_spectrum
keeping the set of states constant. All objects of the model categories of flows and multipointed d-spaces are fibrant. It can be checked that the cylinders
Directed_algebraic_topology
FIBRANT OBJECT
FIBRANT OBJECT
Boy/Male
Arabic
Nature; Creation
Boy/Male
Muslim
Reward
Girl/Female
American, Christian, Dutch, French, German, Jamaican, Latin, Swedish
Vibrant; Life; Alive; Full of Life; Lively
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu, Traditional
Powerful; Hero; Brave; Victorious; Fearless
Boy/Male
Hindu
Sword, Burn
Boy/Male
French, German
Gray-haired; Adventurer
Surname or Lastname
English
English : variant of Farrand.
Boy/Male
Hindu
Powerful, Warrior
Boy/Male
Arabic, Australian
Tree Shadow
Girl/Female
American, British, Chinese, English, French, German, Indian, Latin, Parsi, Portuguese, Romanian, Swedish
Alive; Vibrant; Full of Life; Lively; Life
Boy/Male
Teutonic American English
Firebrand.
Boy/Male
Greek
Guardian of Librans.
Surname or Lastname
English, German, Jewish (Ashkenazic), and Dutch
English, German, Jewish (Ashkenazic), and Dutch : variant of Brand.
Girl/Female
Hindu, Indian, Tamil
Vibrant; Beautiful
Male
French
Variant spelling of French Ferrand, FERRANT means "ardent for peace."
Boy/Male
French
Gray-haired.
Male
English
Variant spelling of English Brandt, BRANT means "blade, sword."
Boy/Male
Arabic, Australian, Muslim
Reward
Boy/Male
Muslim/Islamic
Reward
Boy/Male
French
Gray-haired.
FIBRANT OBJECT
FIBRANT OBJECT
Girl/Female
Indian
Quick, Rapid
Boy/Male
Muslim/Islamic
Successor Descendants
Girl/Female
English French American
Courtyard within castle walls; steward or public official. Surname or given name.
Girl/Female
Muslim
Honorific title, Queen
Boy/Male
Muslim
Shield
Boy/Male
Tamil
Girilal | கிரிலால
Son of mountain
Boy/Male
Indian
Gold
Girl/Female
Scottish
Short.
Boy/Male
Scottish
Bank.
Girl/Female
Indian
Beautiful Flower
FIBRANT OBJECT
FIBRANT OBJECT
FIBRANT OBJECT
FIBRANT OBJECT
FIBRANT OBJECT
a.
Belonging to the fibers of plants.
n.
The state of acquiring or having an excess of fibrin.
n. fem.
A female figurant; esp., a ballet girl.
a.
Smooth; unwrinkled.
a.
Alt. of Brant
n.
A migratory bird or other animal.
a.
Sonant; vibrant; hence, of sounds produced in a cavity, deep-toned; as, sonorous rhonchi.
n.
A brant. See Brant.
a.
Sipping; touching lightly.
a.
Vibrating; tremulous; resonant; as, vibrant drums.
n. masc.
One who dances at the opera, not singly, but in groups or figures; an accessory character on the stage, who figures in its scenes, but has nothing to say; hence, one who figures in any scene, without taking a prominent part.
n.
A white, albuminous, fibrous substance, formed in the coagulation of the blood either by decomposition of fibrinogen, or from the union of fibrinogen and paraglobulin which exist separately in the blood. It is insoluble in water, but is readily digestible in gastric and pancreatic juice.
n.
The act or process of depriving of fibrin.
a.
Migratory.
n.
The state of being vibrant; resonance.
n.
An albuminous body, resembling animal fibrin in composition, found in cereal grains and similar seeds; vegetable fibrin.
a.
Possessed of properties similar to fibrinogen; capable of forming fibrin.
a.
Steep; high.
n.
The white, albuminous mass remaining after washing lean beef or other meat with water until all coloring matter is removed; the fibrous portion of the muscle tissue; flesh fibrin.