# nLab PIE-limit

### Context

#### 2-Category theory

2-category theory

## Structures on 2-categories

#### Limits and colimits

limits and colimits

## (∞,1)-Categorical

### Model-categorical

A PIE-limit is a strict 2-limit which can be constructed from strict products, strict inserters, and strict equifiers. (More precisely, the class of PIE-limits is the saturation of the class containing products, inserters, and equifiers. Any PIE-limit is in particular a flexible limit, and therefore also a (non-strict) 2-limit.

Furthermore, all strict pseudo-limits are PIE-limits, and therefore any strict 2-category which admits all PIE-limits also admits all non-strict 2-limits, although it may not have all strict 2-limits. This is the case, for instance, for the 2-category of strict algebras and pseudo morphisms over a strict 2-monad.

PIE-limits can also be characterized as the coalgebras for a pseudo morphism classifier? comonad, exhibiting them as a 2-categorical version of the notion of rigged limit.

Revised on September 11, 2011 04:30:49 by Mike Shulman (71.136.248.27)