In mathematics, a pseudofunctor ''F'' is a mapping between
2-categories, or from a
category
Category, plural categories, may refer to:
Philosophy and general uses
*Categorization, categories in cognitive science, information science and generally
* Category of being
* ''Categories'' (Aristotle)
* Category (Kant)
* Categories (Peirce) ...
to a
2-category, that is just like a
functor
In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic objects (such as the fundamental group) are associated to topological spaces, an ...
except that
and
do not hold as exact equalities but only up to ''
coherent isomorphism
In mathematics, specifically in homotopy theory and (higher) category theory, coherency is the standard that equalities or diagrams must satisfy when they hold "up to homotopy" or "up to isomorphism".
The adjectives such as "pseudo-" and "lax-" ...
s''.
The
Grothendieck construction associates to a pseudofunctor a
fibered category.
See also
*
Lax functor
In category theory, a discipline within mathematics, the notion of lax functor between bicategories generalizes that of functors between categories.
Let ''C,D'' be bicategories. We denote composition idiagrammatic order A ''lax functor P from ...
*
Prestack (an example of pseudofunctor)
*
Fibered category
References
*C. Sorger
Lectures on moduli of principal G-bundles over algebraic curves
External links
*http://ncatlab.org/nlab/show/pseudofunctor
Functors
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