Higher-Dimensional Algebra III: n-Categories and the . . .

Higher-Dimensional Algebra III: n-Categories and the . . . (1998)

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by John C. Baez , James Dolan

Venue:	MATH
Citations:	70 - 6 self

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Datum	Value	Source
TITLE	Higher-Dimensional Algebra III: n-Categories and the . . .	user correction
AUTHOR NAME	John C. Baez	user correction
AUTHOR AFFIL	Department of Mathematics, University of California	user correction
AUTHOR ADDR	Riverside, California 92521; USA	user correction
AUTHOR NAME	James Dolan	user correction
AUTHOR AFFIL	Department of Mathematics, University of California	user correction
AUTHOR ADDR	Riverside, California 92521; USA	user correction
ABSTRACT	We give a definition of weak n-categories based on the theory of operads. We work with operads having an arbitrary set S of types, or `S-operads', and given such an operad O, we denote its set of operations by elt(O). Then for any S-operad O there is an elt(O)-operad O + whose algebras are S-operads over O. Letting I be the initial operad with a one-element set of types, and defining I 0+ = I, I (i+1)+ = (I i+ ) + , we call the operations of I (n\Gamma1)+ the `n-dimensional opetopes'. Opetopes form a category, and presheaves on this category are called `opetopic sets'. A weak n-category is defined as an opetopic set with certain properties, in a manner reminiscent of Street's simplicial approach to weak !-categories. Similarly, starting from an arbitrary operad O instead of I, we define `n-coherent O-algebras', which are n times categorified analogs of algebras of O. Examples include `monoidal n-categories', `stable n-categories', `virtual n-functors' and `representabl...	user correction - Legacy Corrections
YEAR	1998	INFERENCE
VENUE	MATH	user correction
VENUE TYPE	JOURNAL	INFERENCE
PAGES	145--206	INFERENCE
VOLUME	135	INFERENCE
CITATIONS	30 found	ParsCit 1.0