cobase change

**limits and colimits**
## 1-Categorical
* limit and colimit
* limits and colimits by example
* commutativity of limits and colimits
* small limit
* filtered colimit
* directed colimit
* sequential colimit
* sifted colimit
* connected limit, wide pullback
* preserved limit, reflected limit, created limit
* product, fiber product, base change, coproduct, pullback, pushout, cobase change, equalizer, coequalizer, join, meet, terminal object, initial object, direct product, direct sum
* finite limit
* exact functor
* Kan extension
* Yoneda extension
* weighted limit
* end and coend
## 2-Categorical
* 2-limit
* inserter
* isoinserter
* equifier
* inverter
* PIE-limit
* 2-pullback, comma object
## (∞,1)-Categorical
* (∞,1)-limit
* (∞,1)-pullback
* fiber sequence
### Model-categorical
* homotopy Kan extension
* homotopy limit
* homotopy pullback
* mapping cone
* homotopy fiber
* homotopy colimit
* homotopy pushout
* homotopy cofiber
* mapping cocone

**Cobase change** is another term for pushout of a morphism:

if

$\array{
X &\to & U
\\
\downarrow && \downarrow
\\
Y &\to& Y \sqcup_X U
}$

is a pushout square in some category then the morphism $U \to U \sqcup_X Y$ is the **cobase change** or **cobase extension** of $X \to Y$ along $X \to U$.

- The dual concept is base change.

Last revised on May 19, 2010 at 09:09:08. See the history of this page for a list of all contributions to it.