2-categories, or from a category to a 2-category, that is just like a functor except that F ( f ∘ g ) = F ( f ) ∘ F ( g ) {\displaystyle F(f\circ g)=F(f)\circ...

adjectives such as "pseudo-" and "lax-" are used to refer to the fact equalities are weakened in coherent ways; e.g., pseudo-functor, pseudoalgebra. In...

category Kar ⁡ C {\displaystyle \operatorname {Kar} C} together with a functor s : C → Kar ⁡ C {\displaystyle s:C\to \operatorname {Kar} C} such that...

category) that consists of free T-algebras. lax A lax functor is a generalisation of a pseudo-functor, in which the structural transformations associated...

categorical sum. It follows that any functor which preserves limits will take terminal objects to terminal objects, and any functor which preserves colimits will...

there are forgetful functors A : Ring → Ab M : Ring → Mon which "forget" multiplication and addition, respectively. Both of these functors have left adjoints...

term originally come from category theory, where a monad is defined as a functor with additional structure. Research beginning in the late 1980s and early...

the uniform structure). Any (pseudo)metrizable space is uniformizable since the (pseudo)metric uniformity induces the (pseudo)metric topology. The converse...

nonlinear partial differential equations. This includes generalized functions, pseudo-differential operators, wave front sets, Fourier integral operators, oscillatory...

properties can be dualized. An embedding can also refer to an embedding functor. Ambient space Closed immersion Cover Dimension reduction Flat (geometry)...